Cyclic Cohomology at 40 : Achievements and Future Prospects / edited by A. Connes, [and four others].
 Format
 Book
 Language
 English
 Εdition
 First edition.
 Published/Created

 Providence, Rhode Island : American Mathematical Society, [2023]
 ©2023
 Description
 1 online resource (592 pages)
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 Subject(s)
 Editor
 Series

 Proceedings of symposia in pure mathematics ; Volume 105. [More in this series]
 Proceedings of Symposia in Pure Mathematics Series ; Volume 105
 Summary note
 This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27October 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 Ktheory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory.The reader will find survey articles providing a userfriendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de RhamWitt 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 RhamWitt complex, Fontaine's theory and the FarguesFontaine curve.
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 Includes bibliographical references.
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 Description based on print version record.
 ISBN
 1470472635
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