Smooth Connes--Thom isomorphism, cyclic homology, and equivariant quantisation

2019/07/21 by Sayan Chakraborty, Xiang Tang, Chakraborty, Sayan +3
Mathematics · #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1907.09051

Abstract

Using a smooth version of the Connes--Thom isomorphism in Grensing's bivariant K-theory for locally convex algebras, we prove an equivariant version of the Connes--Thom isomorphism in periodic cyclic homology. As an application, we prove that periodic cyclic homology is invariant with respect to equivariant strict deformation quantization.

Related

• Equivariant local cyclic homology and the equivariant Chern-Connes character
• K-theory of Equivariant Quantization
• Cyclic Theory and the Bivariant Chern-Connes Character
• The Thom isomorphism in bivariant K-theory
• K-Theory Tools For Local and Asymptotic Cyclic Cohomology