Algebraic topology Books
Cambridge University Press The Theory of Cluster Sets
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£36.09
Cambridge University Press Representations and Cohomology v2 Volume 2 Cohomology of Groups and Modules Cambridge Studies in Advanced Mathematics Series Number 31
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£54.14
Cambridge University Press Representations and Cohomology v1 Volume 1 Basic Representation Theory of Finite Groups and Associative Algebras Cambridge Studies in Advanced Mathematics Series Number 30
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£48.44
Cambridge University Press Algebraic Cycles and Motives 344 London
Book SynopsisThese two volumes provide a self-contained account of research on algebraic cycles and motives. Twenty-two contributions from leading figures survey the key research strands, including: Abel-Jacobi/regulator maps and normal functions; Voevodsky's triangulated category of mixed motives; conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups.Table of ContentsPart II. Research Articles: 8. Beilinson's Hodge conjecture with coefficients M. Asakura and S. Saito; 9. On the splitting of the Bloch-Beilinson filtration A. Beauville; 10. Künneth projectors S. Bloch and H. Esnault; 11. The Brill-Noether curve of a stable bundle on a genus two curve S. Brivio and A. Verra; 12. On Tannaka duality for vector bundles on p-adic curves C. Deninger and A. Werner; 13. On finite-dimensional motives and Murre's conjecture U. Jannsen; 14. On the transcendental part of the motive of a surface B. Kahn, J. P. Murre and C. Pedrini; 15. A note on finite dimensional motives S. I. Kimura; 16. Real regulators on Milnor complexes, II J. D. Lewis; 17. Motives for Picard modular surfaces A. Miller, S. Müller-Stach, S. Wortmann, Y.-H.Yang, K. Zuo; 18. The regulator map for complete intersections J. Nagel; 19. Hodge number polynomials for nearby and vanishing cohomology C. Peters and J. Steenbrink; 20. Direct image of logarithmic complexes M. Saito; 21. Mordell-Weil lattices of certain elliptic K3's T. Shioda; 22. Motives from diffraction J. Stienstra.
£61.71
Cambridge University Press Introduction to Compact Riemann Surfaces and Dessins dEnfants 79 London Mathematical Society Student Texts Series Number 79
Book SynopsisFew books on the subject of Riemann surfaces cover the relatively modern theory of dessins d'enfants (children's drawings), which was launched by Grothendieck in the 1980s and is now an active field of research. In this 2011 book, the authors begin with an elementary account of the theory of compact Riemann surfaces viewed as algebraic curves and as quotients of the hyperbolic plane by the action of Fuchsian groups of finite type. They then use this knowledge to introduce the reader to the theory of dessins d'enfants and its connection with algebraic curves defined over number fields. A large number of worked examples are provided to aid understanding, so no experience beyond the undergraduate level is required. Readers without any previous knowledge of the field of dessins d'enfants are taken rapidly to the forefront of current research.Trade Review"Overall the text is very well written and easy to follow, partly due to the abundance of good concrete examples in every single section illustrating concepts from the very basic to the very technical." Aaron D. Wootton, Mathematical ReviewsTable of Contents1. Riemann surfaces and algebraic curves; 2. Riemann surfaces and Fuchsian groups; 3. Belyi's theorem; 4. Dessins d'enfants; References; Index.
£46.54
Cambridge University Press Algebraic Methods in Unstable Homotopy Theory 12 New Mathematical Monographs Series Number 12
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£151.05
Cambridge University Press Induced Representations of Locally Compact Groups 197 Cambridge Tracts in Mathematics Series Number 197
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£84.54
Cambridge University Press Graphs Surfaces and Homology
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£72.20
Cambridge University Press Floer Homology Groups in YangMills Theory 147 Cambridge Tracts in Mathematics Series Number 147
Book SynopsisThe seminal work of Floer has now been placed in a contemporary setting. The author of this monograph writes with the big picture constantly in mind, reviewing current knowledge and predicting future directions. This forms part of the work for which Simon Donaldson was awarded the prestigious Fields Medal.Trade Review'… relatively short but very infomative, modern and clearly written … I stronly recommend the book to both specialists and graduate students'. S. Merkulov, Proceedings of the Edinburgh Mathematical Society'… a compact but very readable account.' Mathematika'… gives a nice account of the theory of an interesting topic in contemporary geometry and topology. It can be strongly recommended …'. EMS NewsletterTable of Contents1. Introduction; 2. Basic material; 3. Linear analysis; 4. Gauge theory and tubular ends; 5. The Floer homology groups; 6. Floer homology and 4-manifold invariants; 7. Reducible connections and cup products; 8. Further directions.
£116.85
Cambridge University Press Poincar Duality Algebras Macaulays Dual Systems and Steenrod Operations 167 Cambridge Tracts in Mathematics Series Number 167
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£105.45
Cambridge University Press Complex Topological KTheory 111 Cambridge Studies in Advanced Mathematics Series Number 111
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£75.04
Cambridge University Press Rigid Cohomology 172 Cambridge Tracts in Mathematics Series Number 172
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£107.35
Cambridge University Press Stable Categories and Structured Ring Spectra
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£104.50
Cambridge University Press Foundations of Stable Homotopy Theory
Book SynopsisThe beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. The appendix containing essential facts on model categories, the numerous examples and the suggestions for further reading make this a friendly introduction to an often daunting subject.Trade Review'The authors have made great efforts to ensure that the book is accessible to those who are not already experts in the area. The topics have been carefully chosen, and the exposition includes not just the technical details but also provides historical and motivational context for many of the important ideas.' Dan Isaksen, MAA Reviews'The stated goal of the authors is to provide an accessible entry point to stable homotopy theory for first-year graduate students. The necessary prerequisites are good undergraduate knowledge of point-set topology and algebraic topology. Barnes and Roitzheim achieve their goal within the first three chapters by discussing a large collection of examples. Included among them are the Spanier-Whitehead category, sequential spectra, the stable homotopy category, and two important functors, namely the suspension and the loop functors.' M. Bona, Choice'This is a useful contribution to the literature. As well as nurturing budding stable homotopy theorists, it could also serve as a resource for researchers whose primary interest is not stable homotopy theory, but who seek an understanding of such techniques.' Geoffrey M. L. Powell, Mathematical Reviews'Especially as it seems to be very carefully written, I expect that it will become a standard textbook in the field.' Julie Bergner, zbMATHTable of ContentsIntroduction; 1. Basics of stable homotopy theory; 2. Sequential spectra and the stable homotopy category; 3. The suspension and loop functors; 4. Triangulated categories; 5. Modern categories of spectra; 6. Monoidal structures; 7. Left Bousfield localisation; Appendix. Model categories; References; Index.
£57.94
Cambridge University Press A Gentle Introduction to Homological Mirror
Book SynopsisOriginating in mathematical physics, homological mirror symmetry reveals deep connections between different areas of geometry and algebra. This book, which is aimed at graduate students, offers a self-contained and accessible introduction to the subject from the perspective of representation theory of algebras and quivers.Table of ContentsPart I. To A∞ and Beyond: 1. Categories; 2. Cohomology; 3. Higher products; 4. Quivers; Part II. A Glance through the Mirror: 5. Motivation from physics; 6. The A-side; 7. The B-side; 8. Mirror symmetry; Part III. Reflections on Surfaces: 9. Gluing; 10. Grading; 11. Stabilizing; 12. Deforming; References; Index.
£42.41
The University of Chicago Press Unstable Modules over the Steenrod Algebra and
Book SynopsisAn account of one of the main directions of algebraic topology, this book focuses on the Sullivan conjecture and its generalizations and applications. Intended to be of use to graduates and algebraic topologists, it gathers work on the theory of modules over the Steenrod algebra.
£30.00