Cyclic Cohomology at 40

Achievements and Future Prospects

Häftad, Engelska, 2023

AvA. Connes,C. Consani,B. I. Dundas,M. Khalkhali,H. Moscovici

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This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27-October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada. Cyclic cohomology, since its discovery forty years ago in noncommutative differential geometry, has become a fundamental mathematical tool with applications in domains as diverse as analysis, algebraic K-theory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory. The reader will find 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. The researcher will find frontier research articles in which the cyclic theory provides a computational tool of great relevance. In particular, in analysis cyclic cohomology index formulas capture the higher invariants of manifolds, where the group symmetries are extended to Hopf algebra actions, and where Lie algebra cohomology is greatly extended to the cyclic cohomology of Hopf algebras which becomes the natural receptacle for characteristic classes. In algebraic topology the cyclotomic structure obtained using the cyclic subgroups of the circle action on topological Hochschild homology gives rise to remarkably significant arithmetic structures intimately related to crystalline cohomology through the de Rham-Witt complex, Fontaine's theory and the Fargues-Fontaine curve.

Produktinformation

Utgivningsdatum2023-11-30
Mått178 x 254 x 33 mm
Vikt481 g
FormatHäftad
SpråkEngelska
SerieProceedings of Symposia in Pure Mathematics
Antal sidor579
FörlagAmerican Mathematical Society
ISBN9781470469771

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Algebra inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Topologi inom Naturvetenskap och teknik

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