Equivariant local cyclic homology and the equivariant Chern-Connes character

2006/08/24 by Christian Voigt, Voigt, Christian
Mathematics · #19D55 #19K35 #19L47 #46A17 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:19D55 #msc:19K35 #msc:19L47 #msc:46A17

paper · pdf · doi:10.48550/arxiv.math/0608609

38 pages

arxiv created 2006/08/24 · openalex publication_date 2006/08/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and Lesniewski as a special case and provides an equivariant extension of the local cyclic theory developped by Puschnigg. As a main result we construct a multiplicative Chern-Connes character for equivariant KK-theory with values in equivariant local cyclic homology.

Related

• A note on the equivariant Chern character in Noncommutative Geometry
• A new description of equivariant cohomology for totally disconnected groups
• Smooth Connes--Thom isomorphism, cyclic homology, and equivariant quantisation
• Cyclic Theory and the Bivariant Chern-Connes Character
• Chern character for totally disconnected groups