Continuous homotopy invariance of bivariant local cyclic homology for \sigma-C^*-algebras

TL;DR

This paper proves that bivariant local cyclic homology remains invariant under continuous homotopies for --algebras, using cylinder constructions and computing the homology of the infinite sphere.

Contribution

It establishes the continuous homotopy invariance of bivariant local cyclic homology for --algebras and computes the homology of the infinite sphere.

Findings

Proves homotopy invariance of local cyclic homology for --algebras.

Shows an isomorphism between smooth and continuous cylinder constructions.

Computes the local cyclic homology of the infinite sphere.

Abstract

We establish the continuous homotopy invariance of bivariant local cyclic homology on the category of all \sigma-C^*-algebras. The argument relies vitally on an isomorphism between the smooth and continuous cylinder constructions using a technical criterion due to Meyer. As a consequence we compute the local cyclic homology of the infinite sphere.