Local cyclic homology of group Banach algebras I: Hyperbolic groups

2016/12/22 by Michael Puschnigg, Puschnigg, Michael
Mathematics · #19D55 #20F67 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:19D55 #msc:20F67

paper · pdf · doi:10.48550/arxiv.1612.07588

arxiv created 2016/12/22 · openalex publication_date 2016/12/22 · arxiv updated 2016/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We calculate the bivariant local cyclic cohomology of the Banach convolution algebra of summable functions on a word-hyperbolic group. Our result implies that the Banach algebraic assembly map in local cyclic homology is an isomorphism for such a group.

Related

• Local cyclic homology of group Banach algebras of "non-positively curved" discrete groups
• Local cyclic homology for nonarchimedean Banach algebras
• K-homological finiteness and hyperbolic groups
• Comparisons between periodic, analytic and local cyclic cohomology
• Equivariant local cyclic homology and the equivariant Chern-Connes character