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Cyclic cohomology at 40 : achievements and future prospects / edited by A. Connes, C. Consani, B. I. Dundas, M. Khalkhali, H. Moscovici.

By: Connes, A [editor.] | Virtual Conference on Cyclic Cohomology at 40 (2021 : Fields Institute for Research in Mathematical Sciences, Toronto (Ont.)) [author.].
Contributor(s): Connes, Alain [editor.] | Consani, Caterina [editor.] | Dundas, B. I. (Bjørn Ian) [editor.] | Khalkhali, Masoud, 1963- [editor.] | Moscovici, Henri, 1944- [editor.].
Material type: TextTextSeries: Proceedings of symposia in pure mathematics, volume 105.Publisher: Providence, Rhode Island : American Mathematical Society, [2023]Description: x, 579 pages; Rs.USD 139.00 25 cms.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781470469771.Subject(s): Homology theory -- Congresses | Algebraic cycles -- Congresses | Noncommutative differential geometry -- Congresses | Number theory -- Zeta and $L$-functions: analytic theory -- Relations with noncommutative geometry | Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Arithmetic varieties and schemes; Arakelov theory; heights | Associative rings and algebras -- Homological methods -- (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) | Associative rings and algebras -- Hopf algebras, quantum groups and related topics -- Hopf algebras and their applications | Associative rings and algebras -- Hopf algebras, quantum groups and related topics -- Bialgebras | $K$-theory -- Higher algebraic $K$-theory -- $K$-theory and homology; cyclic homology and cohomology | Functional analysis -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) -- Noncommutative differential geometry | Global analysis, analysis on manifolds -- Infinite-dimensional manifolds -- Noncommutative geometry (à la Connes) | Quantum theory -- Quantum field theory; related classical field theories -- Noncommutative geometry methods | Quantum theory -- Groups and algebras in quantum theory -- Noncommutative geometryDDC classification: 514/.23 Other classification: 11M55 | 14G40 | 16E40 | 16T05 | 16T10 | 19D55 | 46L87 | 58B34 | 81T75 | 81R60
Contents:
Chern-Connes-Karoubi Character Isomorphism and Algebras of Symbols of Pseudodifferential Operators / A. Baldare, M. Benameur, and V. Nistor -- On Perrot's Index Cocycles / J. Block, N. Higson, and J. Sanchez Jr. -- The Chern-Baum-Connes Assembly Map for Lie Groupoids / P. Carrillo Rouse -- Hochschild Homology, Trace Map and ζ-Cycles / C. Connes and C. Consani -- Cyclic Theory and the Pericyclic Category / C. Connes and C. Consani -- The Image of Bott Periodicity in Cyclic Homology / J. Cuntz -- Applications of Topological Cyclic Homology to Algebraic K-Theory / B. I. Dundas -- Algebraic K-Theory and Generalized Stable Homotopy Theory / D. Gepner -- Cyclic Cohomology and the Extended Heisenberg Calculus of Epstein and Melrose / A. Gorokhovsky and E. van Erp -- Topological Cyclic Homology and the Fargues-Fontaine Curve / L. Hesselholt -- Hopf Cyclic Cohomology and Beyond / M. Khalkhali and Y. Shapiro -- The Hochschild Cohomology of Uniform Roe Algebras / M. Lorentz -- Quantum Differentiability : the Analytical Perspective / E. McDonald, F. Sukochev, and X. Xiong -- Local Cyclic Homology for Nonarchimedean Banach Algebras / R. Meyer and D. Mukherjee -- On the van Est Analogy in Hopf Cyclic Cohomology / H. Moscovici -- Primary and Secondary nvariants of Dirac Operators on G-Proper Manifolds / P. Piazza and X. Tang -- Localization in Hochschild Homology / M. J. Plfaum -- Cyclic Homology and Group Actions / R. Ponge -- Cyclic Cocycles and Quantized Pairings in Materials Science / E. Prodan -- The Periodic Cyclic Homology of Crossed Products / M. Puschnigg -- Trace Expansions and Equivariant Traces on an Algebra of Fourier Integral -- Operators on Rn / A. Savin and E. Schrohe -- Cartan Motion Group and Orbital Integrals / Y. Song and X. Tang -- On Noncommutative Crystalline Cohomology / B. Tsygan -- Cyclic Cocycles and One-Loop Corrections in the Spectral Action / T. D.H. van Nuland and W. van Suijlekom -- ℓ1-Higher Index, ℓ1-Higher rho Invariant and Cyclic Cohomology / J. Wang, Z. Xie, and G. Y.
List(s) this item appears in: 2023-09-08

"Virtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences, Toronto, ON Canada."

Includes bibliographical references.

Chern-Connes-Karoubi Character Isomorphism and Algebras of Symbols of Pseudodifferential Operators / A. Baldare, M. Benameur, and V. Nistor -- On Perrot's Index Cocycles / J. Block, N. Higson, and J. Sanchez Jr. -- The Chern-Baum-Connes Assembly Map for Lie Groupoids / P. Carrillo Rouse -- Hochschild Homology, Trace Map and ζ-Cycles / C. Connes and C. Consani -- Cyclic Theory and the Pericyclic Category / C. Connes and C. Consani -- The Image of Bott Periodicity in Cyclic Homology / J. Cuntz -- Applications of Topological Cyclic Homology to Algebraic K-Theory / B. I. Dundas -- Algebraic K-Theory and Generalized Stable Homotopy Theory / D. Gepner -- Cyclic Cohomology and the Extended Heisenberg Calculus of Epstein and Melrose / A. Gorokhovsky and E. van Erp -- Topological Cyclic Homology and the Fargues-Fontaine Curve / L. Hesselholt -- Hopf Cyclic Cohomology and Beyond / M. Khalkhali and Y. Shapiro -- The Hochschild Cohomology of Uniform Roe Algebras / M. Lorentz -- Quantum Differentiability : the Analytical Perspective / E. McDonald, F. Sukochev, and X. Xiong -- Local Cyclic Homology for Nonarchimedean Banach Algebras / R. Meyer and D. Mukherjee -- On the van Est Analogy in Hopf Cyclic Cohomology / H. Moscovici -- Primary and Secondary nvariants of Dirac Operators on G-Proper Manifolds / P. Piazza and X. Tang -- Localization in Hochschild Homology / M. J. Plfaum -- Cyclic Homology and Group Actions / R. Ponge -- Cyclic Cocycles and Quantized Pairings in Materials Science / E. Prodan -- The Periodic Cyclic Homology of Crossed Products / M. Puschnigg -- Trace Expansions and Equivariant Traces on an Algebra of Fourier Integral -- Operators on Rn / A. Savin and E. Schrohe -- Cartan Motion Group and Orbital Integrals / Y. Song and X. Tang -- On Noncommutative Crystalline Cohomology / B. Tsygan -- Cyclic Cocycles and One-Loop Corrections in the Spectral Action / T. D.H. van Nuland and W. van Suijlekom -- ℓ1-Higher Index, ℓ1-Higher rho Invariant and Cyclic Cohomology / J. Wang, Z. Xie, and G. Y.