Topology Books
MP-AMM American Mathematical Function Theory on Symplectic Manifolds
Book Synopsis
£103.50
American Mathematical Society Manifolds and KTheory
Book SynopsisContains the proceedings of the conference on Manifolds, $K$-Theory, and Related Topics, held in June, 2014. The articles are a collection of research papers featuring recent advances in homotopy theory, $K$-theory, and their applications to manifolds. Topics covered include homotopy and manifold calculus, structured spectra, and their applications to group theory and the geometry of manifolds.Table of Contents G. Arone and M. Ching, Manifolds, K-theory and the calculus of functors J. E. Bergner and P. Hackney, Diagrams encoding group actions on $\Gamma$-spaces S. Chang, S. Weinberger, and G. Yu, Contractible manifolds with exotic positive scalar curvature behavior E. D. Farjoun and Y. Segev, Relative Schur multipliers and universal extensions of group homomorphisms T. G. Goodwillie, Scissors congruence with mixed dimensions J. R. Klein and S. Tilson, On the moduli space of $A_\infty$-structures J. Noel, Nilpotence in the symplectic bordism ring K. E. Pelatt and D. P. Sinha, A geometric homology representative in the space of knots M. Szymik, Brauer spaces for commutative rings and structured ring spectra H. L. Tanaka, Bridgeland stability, 2-Segal spaces, and the Ran space of the line S. Tillmann and M. S. Weiss, Occupants in manifolds.
£109.25
MP-AMM American Mathematical Winding Around
Book SynopsisTrade ReviewThis book covers a lot of ground. But it does so in a clear and careful manner that would make a terrific read for the prepared undergraduate. It is a study in how an intuitive idea can transport one into some deep waters of mathematics, and that is an important story to tell." - John McCleary, Mathematical Reviews"People who teach university-level mathematics for a living often find themselves reading lots of books on the subject. But even for the book-lovers among us, after you've just read about ten linear algebra texts, all of which look like they were stamped from the same cookie cutter, the process can occasionally wear thin. It's very pleasant, then, to stumble across a book that is genuinely unique, that addresses a topic in a way not found elsewhere, and that teaches you something that you didn't know before. It's even nicer when the book in question does a really good job of it, as is the case with the book under review. ...Roe's writing style is succinct, but clear and quite elegant; I could practically hear a British accent as I read the book. This clarity of writing and the numerous appendices help make the book accessible." - MAA OnlineTable of Contents Prelude: Love, hate, and exponentials Paths and homotopies The winding number Topology of the plane Integrals and the winding number Vector fields and the rotation number The winding number in functional analysis Coverings and the fundamental group Coda: The Bott periodicity theorem Linear algebra Metric spaces Extension and approximation theorems Measure zero Calculus on normed spaces Hilbert space Groups and graphs Bibliography Index
£47.70
MP-AMM American Mathematical Quandles
Book SynopsisProvides an accessible introduction to quandle theory for readers with a background in linear algebra. Important concepts from topology and abstract algebra motivated by quandle theory are introduced along the way. Includes elementary self-contained treatments of topics such as group theory, cohomology, knotted surfaces and more.Table of Contents Knots and links Algebraic structures Quandles Quandles and groups Generalizations of quandles Enhancements Generalizd knots and links Bibliography Index
£47.70
MP-AMM American Mathematical Differential Geometry Curves Surfaces
Book SynopsisOffers an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples.Trade ReviewThe book provides an excellent introduction to the differential geometry of curves, surfaces and Riemannian manifolds that should be accessible to a variety of readers… Frankly, this is a great book… even after only two chapters the reader is exposed to a lot of interesting mathematics. If you are looking to teach or learn differential geometry at an introductory level, Differential Geometry Curves—Surfaces—Manifolds is a great resource to have on hand." - Jason M. Graham, MAA ReviewsTable of Contents Notations and prerequisites from analysis Curves in $\mathbb{R}^n$ The local theory of surfaces The intrinsic geometry of surfaces Riemannian manifolds The curvature tensor Spaces of constant curvature Einstein spaces Solutions to selected exercises Bibliography List of notation Index
£46.80
American Mathematical Society Knots Molecules and the Universe An Introduction
Book SynopsisProvides an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas.Trade Review[T]his is a wonderful introduction to geometry and topology and their applications to the sciences. The book contains a unique collection of topics that might entice young readers to continue their academic careers by learning more about the world of mathematics." - Claus Ernst, Zentralblatt MATHTable of Contents Universes: An introduction to the shape of the universe Visualizing four dimensions Geometry and topology of different universes Orientability Flat manifolds Connected sums of spaces Products of spaces Geometries of surfaces Knots: Introduction to knot theory Invariants of knots and links Knot polynomials Molecules: Mirror image symmetry from different viewpoints Techniques to prove topological chirality The topology and geometry of DNA The topology of proteins Index
£62.10
MP-AMM American Mathematical Curvature A Variational Approach
Book SynopsisThe curvature discussed in this paper is a far reaching generalization of the Riemannian sectional curvature. The authors give a unified definition of curvature which applies to a wide class of geometric structures whose geodesics arise from optimal control problems, including Riemannian, sub-Riemannian, Finsler and sub-Finsler spaces.Table of Contents Introduction Part 1. Statements of the results: General setting Flag and growth vector of an admissible curve Geodesic cost and its asymptotics Sub-Riemannian geometry Part 2. Technical tools and proofs: Jacobi curves Asymptotics of the Jacobi curve: equiregular case Sub-Laplacian and Jacobi curves Part 3. Appendix: Appendix A. Smoothness of value function (Theorem $2.19$) Appendix B. Convergence of approximating Hamiltonian systems (Proposition 5.15) Appendix C. Invariance of geodesic growth vector by dilations (Lemma $5.20$) Appendix D. Regularity of $C(t,s)$ for the Heisenberg group (Proposition $5.51$) Appendix E. Basics on curves in Grassmannians (Lemma $3.5$ and $6.5$) Appendix F. Normal conditions for the canonical frame Appendix G. Coordinate representation of flat, rank 1 Jacobi curves (Proposition $7.7$) Appendix H. A binomial identity (Lemma $7.8$) Appendix I. A geometrical interpretation of $\dot c_t$ Bibliography Index.
£61.75
MP-AMM American Mathematical From Frenet to Cartan The Method of Moving Frames
Book SynopsisOffers an introduction to the method of moving frames as developed by Cartan, at a level suitable for beginning graduate students familiar with the geometry of curves and surfaces in Euclidean space. The main focus is on the use of this method to compute local geometric invariants for curves and surfaces in various 3-dimensional homogeneous spaces.Trade ReviewAn excellent and unique graduate level exposition of the differential geometry of curves, surfaces and higher-dimensional submanifolds of homogeneous spaces based on the powerful and elegant method of moving frames. The treatment is self-contained and illustrated through a large number of examples and exercises, augmented by Maple code to assist in both concrete calculations and plotting. Highly recommended." — Niky Kamran, McGill University"The method of moving frames has seen a tremendous explosion of research activity in recent years, expanding into many new areas of applications, from computer vision to the calculus of variations to geometric partial differential equations to geometric numerical integration schemes to classical invariant theory to integrable systems to infinite-dimensional Lie pseudo-groups and beyond. Cartan theory remains a touchstone in modern differential geometry, and Clelland's book provides a fine new introduction that includes both classic and contemporary geometric developments and is supplemented by Maple symbolic software routines that enable the reader to both tackle the exercises and delve further into this fascinating and important field of contemporary mathematics. Recommended for students and researchers wishing to expand their geometric horizons." — Peter Olver, University of MinnesotaTable of Contents Background material: Assorted notions from differential geometry Differential forms Curves and surfaces in homogeneous spaces via the method of moving frames: Homogeneous spaces Curves and surfaces in Euclidean space Curves and surfaces in Minkowski space Curves and surfaces in equi-affine space Curves and surfaces in projective space Applications of moving frames: Minimal surfaces in $\mathbb{E}^3$ and $\mathbb{A}^3$ Pseudospherical surfaces in Backlund's theorem Two classical theorems Beyond the flat case: Moving frames on Riemannian manifolds: Curves and surfaces in elliptic and hyperbolic spaces The nonhomogeneous case: Moving frames on Riemannian manifolds Bibliography Index.
£106.20
MP-AMM American Mathematical Ordered Groups and Topology
Book SynopsisDeals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology.Trade ReviewThe book finds a good balance between being a resource for researchers and a graduate textbook." - Sebastian Wolfgang Hensel, Mathematical Reviews"The diligent and disciplined reader of this thin (<150 pp) book will be rewarded by a lot more than knowledge of ordered groups." - Lee P. Neuwirth, Zentralblatt MATH"Given the huge popularity enjoyed by low dimensional topology these days, and all for good reason, it should make a very positive impact. The book is easy to read and deals with very pretty mathematics." - Michael Berg, MAA ReviewsTable of Contents Orderable groups and their algebraic properties Hölder’s theorem, convex subgroups and dynamics Free groups, surface groups and covering spaces Knots Three-dimensional manifolds Foliations Left-orderings of the braid groups Groups of homeomorphisms Conradian left-orderings and local indicability Spaces of orderings Bibliography
£108.00
MP-AMM American Mathematical Topological Complexity and Related Topics
Book SynopsisTopological complexity is a numerical homotopy invariant, defined by Farber in the early twenty-first century as part of a topological approach to the motion planning problem in robotics. This volume contains survey articles and original research papers on topological complexity and its many generalizations and variants, to give a snapshot of contemporary research on this exciting topic.Table of Contents Survey Articles: A. Angel and H. Colman, Equivariant topological complexities J. Carrasquel, Rational methods applied to sectional category and topological complexity D. C. Cohen, Topological complexity of classical configuration spaces and related objects P. Pavesic, A topologist's view of kinematic maps and manipulation complexity Research Articles: D. M. Davis, On the cohomology classes of planar polygon spaces J.-P. Doeraene, M. El Haouari, and C. Ribeiro, Sectional category of a class of maps L. Fernandez Suarez and L. Vandembroucq, Q-topological complexity N. Fieldsteel, Topological complexity of graphic arrangements J. Gonzalez, M. Grant, and L. Vandembroucq, Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes J. Gonzalez and B. Gutierrez, Topological complexity of collision-free multi-tasking motion planning on orientable surfaces M. Grant and D. Recio-Mitter, Topological complexity of subgroups of Artin's braid groups.
£102.60
MP-AMM American Mathematical Cornered Heegaard Floer Homology
Book SynopsisThe authors construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.Table of Contents Introduction Some abstract 2-algebra More 2-algebra: bending and smoothing Some homological algebra of 2-modules The algebras and algebra-modules The cornering module-2-modules The trimodules $\mathsf{T}_{DDD}$ and $\mathsf{T}_{DDA}$ Cornered 2-modules for cornered Heegaard diagrams Gradings Practical computations The nilCoxeter planar algebra Bibliography.
£64.80
MP-AMM American Mathematical Cantor Minimal Systems
Book SynopsisTable of Contents An example: A tale of two equivalence relations Basics: Cantor sets and orbit equivalence Bratteli diagrams: Generalizing the example The Bratteli-Vershik model: Generalizing the example The Bratteli-Vershik model: Completeness Etale equivalence relations: Unifying the examples The $D$ invariant The Effros-Handelman-Shen theorem The Bratteli-Elliott-Krieger theorem Strong orbit equivalence The $D_m$ invariant The absorption theorem The classification of AF-equivalence relations The classification of $\mathbb{Z}$-actions Examples Bibliography Index of terminology Index of notation
£55.80
MP-AMM American Mathematical Probabilistic Methods in Geometry Topology and
Book SynopsisContains the proceedings of the CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, held in 2016 at the Centre de Recherches Mathematiques. This volume covers developments in active research areas at the interface of Probability, Semiclassical Analysis, Mathematical Physics, Theory of Automorphic Forms and Graph Theory.Table of Contents L. Chen and N. Shu, A geometric treatment of log-correlated Gaussian free fields S. Eswarathasan, Tangent nodal sets for random spherical harmonics J. Friedman, Formal zeta function expansions and the frequency of Ramanujan graphs D. Jakobson, T. Langsetmo, I. Rivin, and L. Turner, Rank and Bollobas-Riordan polynomials: Coefficient measures and zeros V. Konakov, S. Menozzi, and S. Molchanov, The Brownian motion on $\mathrm{Aff}(\mathbb{R})$ and quasi-local theorems N. Laaksonen, Quantum limits of Eisenstein series in $\mathbb{H}^3$ F. Macia and G. Riviere, Observability amd quantum limits for the Schrodinger equation on $\mathbb{S}^d$ M. Rossi, Random nodal lengths and Wiener chaos L. Silberman and A. Venkatesh, Entropy bounds and quantum unique ergodity for Hecke eigenfunctions on division algebras.
£103.50
MP-AMM American Mathematical New Complex Analytic Methods in the Study of
Book SynopsisThe aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in $\mathbb{R}^n$ for any $n\ge 3$.
£68.40
MP-AMM American Mathematical Localization for THHku and the Topological
Book SynopsisThe authors develop a theory of $THH$ and $TC$ of Waldhausen categories and prove the analogues of Waldhausen's theorems for $K$-theory. They resolve the longstanding confusion about localization sequences in $THH$ and $TC$, and establish a specialized devissage theorem.
£67.50
MP-AMM American Mathematical Degree Theory of Immersed Hypersurfaces
Book SynopsisThe authors develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function. They apply this theory to count the (algebraic) number of immersed hyperspheres in various cases.
£68.40
MP-AMM American Mathematical Introduction to the Theory of Valuations
Book SynopsisTable of Contents Basic definitions and examples McMullen's decomposition theorem Valuations on the line McMullen's description of $(n-1)$-homogeneous valuations The Klain-Schneider characterization of simple valuations Digression on the theory of generalized functions on manifolds The Goodey-Weil imbedding Digression on vector bundles The irreducibility theorem Further developments Bibliography
£44.06
MP-AMM American Mathematical GromovWitten Theory of Quotients of Fermat
Book Synopsis
£68.40
MP-AMM American Mathematical Topology and Geometry of Biopolymers
Book SynopsisContains the proceedings of the AMS Special Session on Topology of Biopolymers, held April 2018, at Northeastern University. The papers cover recent results on the topology and geometry of DNA and protein knotting using techniques from knot theory, spatial graph theory, differential geometry, molecular simulations, and laboratory experimentation.Table of Contents The topology and geometry of DNA: J. M. Fogg and L. Zechiedrich, Beyond the static DNA model of Watson and Crick P. Liu, R. Polischuk, Y. Diao, and J. Arsuaga, Characterizing the topology of kinetoplast DNA using random knotting A. Kasman and B. LeMesurier, Did sequence dependent geometry influence the evolution of the genetic code? T. Deguchi and E. Uehara, Topological sum rules in the knotting probabilities of DNA D. Buck and D. O'Donnol, Knotting of replication intermediates is narrowly restricted A. H. Moore and M. Vazquez, Recent advances on the non-coherent band surgery model for site-specific recombination The topology and geometry of proteins: S. E. Jackson, Why are there knots in proteins? A. Nunes and P. F. N. Faisca, Knotted proteins: Tie etiquette in structural biology D. Goundaroulis, J. Dorier, and A. Stasiak, Knotoids and protein structure K. C. Millett, Topological linking and entanglement in proteins E. Panagiotou and K. W. Plaxco, A topological study of protein folding kinetics.
£96.30
MP-AMM American Mathematical Goodwillie Approximations to Higher Categories
Book SynopsisConstructs a Goodwillie tower of categories which interpolates between the category of pointed spaces and the category of spectra. This tower of categories refines the Goodwillie tower of the identity functor in a precise sense.
£68.40
MP-AMM American Mathematical Virtual Fundamental Cycles in Symplectic Topology
Book SynopsisBrings together three approaches to constructing the “virtual” fundamental cycle for the moduli space of pseudo-holomorphic curves. All approaches are based on the idea of local Kuranishi charts for the moduli space. The book offers a comprehensive understanding of the details of these constructions and the assumptions under which they can be made.
£101.70
MP-AMM American Mathematical Ktheory in Algebra Analysis and Topology
Book SynopsisContains the proceedings of the ICM 2018 satellite school and workshop $K$-theory conference in Argentina. The volume showcases current developments in $K$-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections.Table of Contents P. Bressler, A. Gorokhovsky, R. Nest, and B. Tsygan, Comparison of spaces associated to DGLA via higher holonomy U. Bunke, A. Engel, D. Kasprowski, and C. Winges, Equivariant coarse homotopy theory and coarse algebraic K-homology A. Buss, S. Echterhoff, and R. Willett, Injectivity, crossed products, and amenable group actions L. Hesselholt and T. Nikolaus, Algebraic $K$-theory of planar cuspidal curves D. Juan-Pineda, On $NK_0$ of the group of quaternions M. Karoubi and C. Weibel, The Witt group of real surfaces A. Krishna and H. P. Sarwar, Negative $K$-theory and Chow group of monoid algebras S. T. Melo, The principal-symbol index map for an algebra of pseudodifferential operators R. Meyer, A more general method to classify up to equivariant KK-equivalence II: Computing obstruction classes A. Neeman, Grothendieck duality made simple J. Park, Calculus of absolute Kahler forms and Milnor $K$-theory G. Tabuada, Noncommutative counterparts of celebrated conjectures R. Willett, Bott periodicity and almost commuting matrices.
£94.50
MP-AMM American Mathematical Noncommutative Geometry Quantum Fields and
Book SynopsisThe unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role.Trade Review...the authors manage very well in filtering and presenting the central ideas whilst including a rich and precise list of references to the literature. ...will undoubtedly serve as an inspiration to the formidable mathematical question on the structure of the following two spaces: spacetime and the space of primes."" - Mathematical ReviewsTable of Contents Quantum fields, noncommutative spaces, and motives The Riemann zeta function and noncommutative geometry Quantum statistical mechanics and Galois symmetries Endomotives, thermodynamics, and the Weil explicit formula Appendix Bibliography Index.
£78.30
MP-AMM American Mathematical Differential Geometry and Its Applications
Book SynopsisStudies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole.Trade Review... There is a good deal to like about this book: the writing is lucid, drawings and diagrams are plentiful and carefully done, and the author conveys a contagious sense of enthusiasm for his subject."" - William J. Satzer, MAA Reviews
£49.40
MP-AMM American Mathematical Sutured ECH is a Natural Invariant
Book Synopsis
£67.50
MP-AMM American Mathematical Dynamics Topology and Numbers
Book SynopsisContains the proceedings of the conference Dynamics: Topology and Numbers, held in July 2018. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics.Table of Contents L. Snoha, The life and mathematics of Sergii Kolyada I. Kolyada, A. Blokh, and L. Snoha, Recollections about Sergii Kolyada P. Moree, Sergiy and the MPIM Y. I. Manin and M. Marcolli, Homotopy types and geometries below ${\rm Spec}(\mathbb{Z})$ A. Fel'shtyn and M. Zietek, Dynamical zeta functions of Riedemeister type and representations spaces O. Jenkinson and M. Pollicott, Rigorous dimension estimates for Cantor sets arising in Zaremba theory P. Colognese and M. Pollicott, Volume growth for infinite graphs and translation surfaces J. Byszewski, G. Cornelissen, M. Houben, and L. Van Der Meijden, Dynamically affine maps in positive characteristic S. Kolyada, M. Misiurewicz, and L. Snoha, Special $\alpha$-limit sets E. Shi and X. Ye, Equicontinuity of minimal sets for amenable group actions on dendrites E. Akin, E. Glasner, and B. Weiss, On weak rigidity and weakly mixing enveloping semigroups A. Ganguly and A. Ghosh, The inhomogenous Sprindzhuk conjecture over a local field of positive characteristic A. Blokh, L. Oversteegen, and V. Timorin, Dynamical generation of parameter laminations P. Oprocha, T. Yu, and Guohua Zhang, Multi-sensitivity, multi-transitivity and $\delta$-transitivity R. Sharp, Convergence of zeta functions for amenable group extensions of shifts S. Bezuglyi and O. Karpel, Invariant measures for Cantor dynamical systems M. Kapovich, Periods of abelian differentials and dynamics J. Riedl and D. Schleicher, Crossed renormalization of quadratic polynomials.
£94.50
MP-AMM American Mathematical Tits Polygons
Book Synopsis
£67.50
American Mathematical Society Complex Numbers and Geometry
Book SynopsisDemonstrates that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem.Trade ReviewProvides a self-contained introduction to complex numbers and college geometry written in an informal style with an emphasis on the motivation behind the ideas ... The author engages the reader with a casual style, motivational questions, interesting problems and historical notes."" - Mathematical Reviews
£41.75
MP-AMM American Mathematical Floer Cohomology and Flips
Book SynopsisShow that blow-ups or reverse flips (in the sense of the minimal model program) of rational symplectic manifolds with point centers create Floer-non-trivial Lagrangian tori. These results are part of a conjectural decomposition of the Fukaya category of a compact symplectic manifold with a singularity-free running of the minimal model program.
£67.50
MP-AMM American Mathematical A Cornucopia of Quadrilaterals
Book SynopsisCollects and organises hundreds of beautiful and surprising results about four-sided figures. The book contains hundreds of challenging four-sided problems. Instructors of number theory, combinatorics, analysis, and geometry will find examples and problems to enrich their courses.Table of Contents Simple quadrilaterals Quadrilaterals and their circles Diagonals of quadrilaterals Properties of trapezoids Applications of trapezoids Garfield trapezoids and rectangles Parallelograms Rectangles Squares Special quadrilaterals Quadrilateral numbers Solutions to the Challenges A quadrilateral glossary Credits and permissions Bibliography Index.
£46.80
MP-AMM American Mathematical Topological Persistence in Geometry and Analysis
Book SynopsisThe theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research.Table of Contents A primer of persistence modules: Definition and first examples Barcodes Proof of the isometry theorem What can we read from a barcode? Applications to metric geometry and function theory: Applications of Rips complexes Topological function theory Persistent homology in symplectic geometry: A concise introduction to symplectic geometry Hamiltonian persistence modules Symplectic persistence modules Bibliography Notation index Subject index Name index.
£43.16
American Mathematical Society Horocycle Dynamics New Invariants and Eigenform
Book SynopsisView the abstract.
£67.45
MP-AMM American Mathematical Partial Compactification of Monopoles and Metric
Book SynopsisView the abstract.
£68.40
MP-AMM American Mathematical The Regularity of the Linear Drift in Negatively
Book SynopsisView the abstract.
£67.45
MP-AMM American Mathematical Integrability Quantization and Geometry The Set
Book SynopsisOffers a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.Table of Contents Part I. Integrable Systems: K. Aleshkin and K. Saito, Primitive forms without higher residue structure and integrable hierarchies (I) M. Alkadhem, G. Antoniou, and M, Feigin, Solutions of $BC_n$ type of WDVV equations P. P. Boalch, Topology of the Stokes phenomenon G. Cotti and A. Varchenko, Equivariant quantum differential equation and qKZ equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and $\mathcyr{B}$-theorem L. David and C. Hertling, Meromorphic connections over F-manifolds G. Jorjadze and S. Theisen, Canonical maps and integrability in $T\bar{T}$ deformed 2d CFTs I. Krichever and A. Varchenko, Incarnations of XXX $\widehat{\mathfrak{sl}_N}$ Bethe ansatz equations and integrable hierarchies F. Magri, The Kowalewski separability conditions O. Mokhov and N. A. Strizhova, On the Liouville integrable reduction of the associativity equations in the case of three primary fields S. M. Natanzon and A. Yu. Orlov, Hurwitz numbers from matrix integrals over Guassian measure N. Reshetikhin, Spin Calogero-Moser models on symmetric spaces M. Semenov-Tian-Shansky, Quantum toda lattice: A challenge for representation theory A. O. Smirnov, M. V. Pavlov, V. B. Matveev, and V. S. Gerdjikov, Finite-gap solutions of the Mikhalev equation I. A. B. Strachan, Flat coordinates on orbit spaces: From Novikov algebras to cyclic quotient singularities K. Takasaki, Cubic Hodge integrals and integrable hierarchies of Volterra type G. Tian and G. Xu, Gauged Witten equation and adiabatic limit Part II. Quantum Theories and Algebraic Geometry: T. Bridgeland, Geometry from Donaldson-Thomas invariants V. M. Buchstaber and A. P. Veselov, Fricke identities, Frobenius $K$-characters and Markov equation I. Cherednik, On Harish-Chandra theory of global nonsymmetric functions N. C. Combe and Y. I. Manin, Symmetries of genus zero modular operad R. Coquereaux and J.-B. Zuber, On Schur problem and Kostka numbers P. Etingof, E. Frenkel, and D. Kazhdan, An analytic version of the Langlands correspondence for complex curves D. Gaiotto, T. Johnson-Freyd, and E. Witten, A note on some minimally supersymmetric models in two dimensions O. Garcia-Prada and D. Salamon, A moment map interpretation of the Ricci form, Kahler-Einstein structures, and Teichmuller spaces E. Getzler and S. W. Pohorence, Global gauge conditions in the Batalin-Vilkovisky formalism V. Golyshev and D. Zagier, Interpolated Apery numbers, quasiperiods of modular forms, and motivic gamma functions Y.-P. Lee, H.-W. Lin, and C.-L. Wang, Quantum flips I: Local model M. Marcolli, Aspects of $p$-adic geometry related to entanglement entropy S. Merkulov, Grothendieck-Teichmuller group, operads and graph complexes: A survey O. Ogievetsky and S. Shlosman, Platonic compounds of cylinders.
£195.30
MP-AMM American Mathematical Integrability Quantization and Geometry I.
Book SynopsisOffers a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.Table of Contents K. Aleshkin and K. Saito, Primitive forms without higher residue structure and integrable hierarchies (I) M. Alkadhem, G. Antoniou, and M, Feigin, Solutions of $BC_n$ type of WDVV equations P. P. Boalch, Topology of the Stokes phenomenon G. Cotti and A. Varchenko, Equivariant quantum differential equation and qKZ equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and $\mathcyr{B}$-theorem L. David and C. Hertling, Meromorphic connections over F-manifolds G. Jorjadze and S. Theisen, Canonical maps and integrability in $T\bar{T}$ deformed 2d CFTs I. Krichever and A. Varchenko, Incarnations of XXX $\widehat{\mathfrak{sl}_N}$ Bethe ansatz equations and integrable hierarchies F. Magri, The Kowalewski separability conditions O. Mokhov and N. A. Strizhova, On the Liouville integrable reduction of the associativity equations in the case of three primary fields S. M. Natanzon and A. Yu. Orlov, Hurwitz numbers from matrix integrals over Guassian measure N. Reshetikhin, Spin Calogero-Moser models on symmetric spaces M. Semenov-Tian-Shansky, Quantum toda lattice: A challenge for representation theory A. O. Smirnov, M. V. Pavlov, V. B. Matveev, and V. S. Gerdjikov, Finite-gap solutions of the Mikhalev equation I. A. B. Strachan, Flat coordinates on orbit spaces: From Novikov algebras to cyclic quotient singularities K. Takasaki, Cubic Hodge integrals and integrable hierarchies of Volterra type G. Tian and G. Xu, Gauged Witten equation and adiabatic limit.
£108.00
MP-AMM American Mathematical Integrability Quantization and Geometry II.
Book SynopsisOffers a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.Table of Contents T. Bridgeland, Geometry from Donaldson-Thomas invariants V. M. Buchstaber and A. P. Veselov, Fricke identities, Frobenius $K$-characters and Markov equation I. Cherednik, On Harish-Chandra theory of global nonsymmetric functions N. C. Combe and Y. I. Manin, Symmetries of genus zero modular operad R. Coquereaux and J.-B. Zuber, On Schur problem and Kostka numbers P. Etingof, E. Frenkel, and D. Kazhdan, An analytic version of the Langlands correspondence for complex curves D. Gaiotto, T. Johnson-Freyd, and E. Witten, A note on some minimally supersymmetric models in two dimensions O. Garcia-Prada and D. Salamon, A moment map interpretation of the Ricci form, Kahler-Einstein structures, and Teichmuller spaces E. Getzler and S. W. Pohorence, Global gauge conditions in the Batalin-Vilkovisky formalism V. Golyshev and D. Zagier, Interpolated Apery numbers, quasiperiods of modular forms, and motivic gamma functions Y.-P. Lee, H.-W. Lin, and C.-L. Wang, Quantum flips I: Local model M. Marcolli, Aspects of $p$-adic geometry related to entanglement entropy S. Merkulov, Grothendieck-Teichmuller group, operads and graph complexes: A survey O. Ogievetsky and S. Shlosman, Platonic compounds of cylinders.
£108.00
American Mathematical Society Icons of Mathematics
Book SynopsisPresents twenty icons of mathematics, that is, geometrical shapes such as the right triangle, the Venn diagram, and the yang and yin symbol, and explores mathematical results associated with them. As with their previous books (Charming Proofs, When Less is More, Math Made Visual) proofs are visual whenever possible.Trade ReviewImages, whether real or in the imagination, are a foundational component of mathematics. In this book the authors begin with 20 of the most fundamental real images and develop a series of consequences with proofs based on those images. A short section of challenge problems are given at the end of each chapter with solutions included in an appendix. Some of the 20 iconic images used are: Two circles, Venn diagrams, Polygons with circles, Right triangles, The semicircle, and The bride's chair. A set of works in geometry, the book could be used as a text in a college course in Euclidean geometry; it is an excellent study item to prepare high school teachers of geometry. People currently teaching high school geometry will find it a valuable resource for more challenging problems to present to the students. Others with just an interest in geometry will find it worthy of an in-depth look."" - Charles Ashbacher, Journal of Recreational Mathematics""Treating mainly elementary geometry, this book can be enjoyed by amateurs and professionals alike. All that is needed is some secondary background in Euclidean geometry and trigonometry, seasoned with imagination. The twenty ""icons,"" or geometrical diagrams, some of historical interest, act as an organizing principle. Each sets the stage for a chain of related results, most established in an informal manner by standard Euclidean arguments, algebraic and trigonometric manipulations, and ""proofs without words"" using partitions and figure-shifting. Frequent digressions provide historical background, short biographies, notes about mathematical artefacts and information about how geometry intervenes in everyday life. Apart from standard results on circles and triangles, the authors discuss a variety of topics, including Dido's isoperimetric problem, regular solids, reptiles, cevians, the butterfly theorem, Reuleaux polygons, polygonal numbers, triangulation of polygons, the cycloid, star polygons, self-similarity, and spirals and tilings. This book is particularly recommended for secondary mathematics students... "" - E.J. Barbeau, Mathematical Reviews""Certain images in mathematics prompt an immediate reaction, similar to the way a smell can trigger a memory. In this provocative collection, the images chosen have what Alsina (Polytechnic Univ. of Catalonia, Spain) and Nelsen (Lewis and Clark College) believe to be iconic value, that is, they are universally recognized. The authors identify and name each image, and explain the image's history, everyday appearance, and mathematical roles. Along with the classical results, they consider generalizations that are not well known but very engaging. For example, cevians make the list for their role in identifying the many special points of triangles. The authors also discuss Stewart's theorem and a generalization to circles. Each of the volume's 20 chapters ends with a ""Challenges"" section. This unusual work is a welcome addition to any library; all readers will find something to inform and even delight them."" - J. McCleary, CHOICE
£51.30
American Mathematical Society Curvature of Space and Time with an Introduction
Book SynopsisIntroduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations.Table of Contents Introduction to Riemannian geometry Differential calculus with tensors Curvature General relativity Introduction to geometry analysis Bibliography Index
£51.30
MP-AMM American Mathematical Geometry and Topology of Manifolds Surfaces and
Book SynopsisPresents a novel approach to differential topology. The book’s main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal.Table of Contents Topological surfaces Algebraic topology Riemannian geometry Constant curvature Complex geometry Global analysis Index Symbols.
£70.20
MP-AMM American Mathematical Topology Through Inquiry
Book SynopsisOffers a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat.Table of Contents Introduction: The enchanting world of topology Point-set topology: Cardinality: To infinity and beyond Topological spaces: Fundamentals Bases, subspaces, products: Creating new spaces Separation properties: Separating this from that Countable features of spaces: Size restrictions Compactness: The next best thing to being finite Continuity: When nearby points stay together Connectedness: When things don't fall into pieces Metric spaces: Getting some distance Algebraic and geometric topology: Transition from point-set topology to algebraic and geometric topology: Similar strategies, different domains Classification of 2-manifolds: Organizing surfaces Fundamental group: Capturing holes Covering spaces: Layering it on Manifolds, simpleces, complexes, and triangulability: Building blocks Simplicial $\mathbb{Z}_2$-homology: Physical algebra Applications of $\mathbb{Z}_2$-homology: A topological superhero Simplicial $\mathbb{Z}$-homology: Getting oriented Singular homology: Abstracting objects to maps The end: A beginning--reflections on topology and learning Appendix: Group theory background Index
£59.40
American Mathematical Society Geometry and the Imagination
Book SynopsisThis remarkable book has endured as a masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer-even after more than half a century. The book is overflowing with mathematical ideas, which are explained clearly and elegantly, and above all, with penetrating insight.Trade ReviewThis book is a masterpiece -- a delightful classic that should never go out of print. -- MAA Reviews [This] superb introduction to modern geometry was co-authored by David Hilbert, one of the greatest mathematicians of the 20th century. -- Steven StrogatzTable of Contents The simplest curves and surfaces Regular systems of points Projective configurations Differential geometry Kinematics Topology Index.
£54.90
MP-AMM American Mathematical Convexity of Singular Affine Structures and
Book SynopsisA systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. Peculiarly, these systems' base spaces are still smooth manifolds, analogous to the toric case, but their associated integral affine structures are singular, with non-trivial monodromy, due to focus singularities.
£68.40
MP-AMM American Mathematical Organized Collapse An Introduction to Discrete
Book SynopsisProvides a gentle introduction into discrete Morse theory. Using a combinatorial approach, the author emphasizes acyclic matchings as the central object of study. The first two parts of the book can be used as a stand-alone introduction to homology, the last two parts delve into the core of discrete Morse theory.Table of Contents Preamble Preface The idea of homology The idea of discrete Morse theory A sample application How to use this book Prerequisites Guide to the literature Part 1 . Introduction to Homology Chapter 1. The First Steps Chapter 2. Simplicial Homology Chapter 3. Beyond the Simplicial Setting Part 2 . Further Aspects of Homology Theory Chapter 4. Category of Chain Complexes Chapter 5. Chain Homotopy Chapter 6. Connecting Homomorphism Chapter 7. Singular Homology Chapter 8. Cellular Homology Suggested further reading for Parts 1 and 2 Part 3 . Basic Discrete Morse Theory Chapter 9. Simplicial Collapses Chapter 10. Organizing Collapsing Sequences Chapter 11. Internal Collapses and Discrete Morse Theory Chapter 12. Explicit Homology Classes Associated to Critical Cells Chapter 13. The Critical Morse Complex Chapter 14. Implications and Variations Suggested further reading for Part 3 Part 4 . Extensions of Discrete Morse Theory Chapter 15. Algebraic Morse Theory Chapter 16. Discrete Morse Theory for Posets Chapter 17. Discrete Morse Theory for CW Complexes Chapter 18. Discrete Morse Theory and Persistence Suggested further reading for Part 4 Index List of Figures List of Tables Bibliography Index Preview Material Preface Table of Contents
£70.20
American Mathematical Society Extrinsic Geometric Flows
Book SynopsisProvides an extensive introduction to a few of the most prominent extrinsic flows, namely the curve shortening flow, the mean curvature flow, the Gauss curvature flow, the inverse-mean curvature flow, and fully nonlinear flows of mean curvature and inverse-mean curvature type.Trade ReviewThis textbook, written by four experts in the field, offers an authoritative introduction and overview to the topic of extrinsic geometric flows. It will serve well as a primary text for a graduate student who already has background knowledge of differential geometry and (some) partial differential equations. It will also serve as a useful reference for experts in the field."" - John Ross, Southwestern UniversityTable of Contents The heat equation Introduction to curve shortening The Gage-Hamilton-Grayson theorem Self-similar and ancient solutions Hypersurfaces in Euclidean space Introduction to mean curvature flow Mean curvature flow of entire graphs Huisken's theorem Mean convex mean curvature flow Monotonicity formulae Singularity analysis Noncollapsing Self-similar solutions Ancient solutions Gauss curvature flows The affine normal flow Flows by superaffine powers of the Gauss curvature Fully nonlinear curvature flows Flows of mean curvature type Flows of inverse-mean curvature type Bibliography Index
£77.40
MP-AMM American Mathematical Smooth Homotopy of InfiniteDimensional Cinfty
Book SynopsisWe use homotopical algebra (or abstract homotopical methods) to study smooth homotopical problems of infinite-dimensional C$C^{\infty }$-manifolds in convenient calculus. More precisely, we discuss the smoothing of maps, sections, principal bundles, and gauge transformations.
£68.40
MP-AMM American Mathematical Fundamental Factorization of a GLSM Part I
Book SynopsisWe define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases these invariants recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using cosection localization as well as the FJRW type invariants constructed by Polishchuk-Vaintrob.
£68.40
MP-AMM American Mathematical Asymptotic Counting in Conformal Dynamical
Book Synopsis
£67.50
