Description
Book SynopsisPresents survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc, in which cyclic homology plays the role of a unifying theme.
Table of Contents
- A. Baldare, M. Benameur, and V. Nistor, Chern-Connes-Karoubi character isomorphisms and algebras of symbols of pseudodifferential operators
- J. Block, N. Higson, and J. Sanchez Jr., On Perrot's index cocycles
- P. Carrillo Rouse, The Chern-Baum Connes assembly map for Lie groupoids
- A. Connes and C. Consani, Hochschild homology, trace map and $\zeta$-cycles
- A. Connes and C. Consani, Cyclic theory and the pericyclic category
- J. Cuntz, The image of Bott peridocity in cyclic homology
- B. I. Dundas, Applications of topological cyclic homology to algebraic $K$-theory
- D. Gepner, Algebraic $K$-theory and generalized stable homotopy theory
- A. Gorokhovsky and E. van Erp, Cyclic cohomology and the extended Heisenberg calculus of Epstein and Melrose
- L. Hesselholt, Topological cyclic homology and the Fargues-Fontaine curve
- M. Khalkhali and I. Shapiro, Hopf cyclic cohomology and beyond
- M. Lorentz, The Hochschild cohomology of uniform Roe algebras
- E. McDonald, F. Sukochev, and X. Xiong, Quantum differntiability-The analytical perspective
- R. Meyer and D. Mukherjee, Local cyclic homology for nonarchimedean Banach algebras
- H. Moscovici, On the van Est analogy in Hopf cyclic cohomology
- P. Piazza and X. Tang, Primary and secondary invariants of Dirac operators on $G$-proper manifolds
- M. J. Pflaum, Localization in Hochschild homology
- R. Ponge, Cyclic homology and group actions
- E. Prodan, Cyclic cocycles and quantized pairings in materials science
- M. Puschnigg, Periodic cyclic homology of crossed products
- A. Savin and E. Schrohe, Trace expansions and equivariant traces on an algebra of Fourier integral operators on $\mathbb{R}^n$
- Y. Song and X. Tang, Carton motion group and orbital integrals
- B. Tsygan, On noncommutative crystalline cohomology
- T. D. H. Van Nuland and W. D. van Suijlekom, Cyclic cocycles and one-loop corrections in the spectral action
- J. Wang, Z. Xie, and G. Yu, $\ell^1$-higher index, $\ell^1$-higher rho invariant and cyclic cohomology.
