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

TL;DR

This paper establishes an equivariant version of the Connes--Thom isomorphism in cyclic homology using smooth bivariant K-theory, demonstrating invariance of cyclic homology under equivariant deformation quantization.

Contribution

It introduces a smooth version of the Connes--Thom isomorphism in bivariant K-theory and applies it to show invariance of cyclic homology under equivariant deformation quantization.

Findings

Proves an equivariant Connes--Thom isomorphism in periodic cyclic homology.

Shows cyclic homology invariance under equivariant strict deformation quantization.

Extends classical isomorphism results to a smooth, equivariant setting.

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.