KK-fibrations arising from Rieffel deformations

TL;DR

This paper demonstrates that the bundle maps in the continuous field associated with Rieffel deformations of C*-algebras are KK-equivalences, using a 2-cocycle twisting approach and RKK-fibrations, advancing the understanding of deformation theory.

Contribution

It introduces a novel method to prove KK-equivalence of bundle maps in Rieffel deformations via 2-cocycle twisting and RKK-fibrations, providing new insights into deformation theory.

Findings

Bundle maps are KK-equivalences for all parameters h in [0,1].

The approach uses 2-cocycle twisting and RKK-fibrations.

Results deepen understanding of Rieffel deformation structures.

Abstract

The bundle map $\pi_{h}: \Gamma((A_{tJ})_{t\in [0,1]})\lra A_{hJ}$, for every $h\in [0,1]$, of the continuous field $(A_{tJ})_{t\in [0,1]}$ associated to the Rieffel deformation $A_{J}$ of a C*-algebra $A$ is shown to be a KK-equivalence by using a 2-cocycle twisting approach and RKK-fibrations.