Twisted Roe algebras and their $K$-theory
K-Theory and Homology
2025-05-27 v2 Functional Analysis
Operator Algebras
Abstract
In this paper, we introduce a notion of twisted Roe algebra and a twisted coarse Baum-Connes conjecture with coefficients. We will study the basic properties of twisted Roe algebras, including a coarse analogue of the imprimitivity theorem for metric spaces with a structure of coarse fibrations. We show that the twisted coarse Baum-Connes conjecture with coefficients holds for a metric space with a coarse fibration structure when the base space and the fiber satisfy the twisted coarse Baum-Connes conjecture with coefficients. As an application, the coarse Baum-Connes conjecture holds for a finitely generated group which is an extension of coarsely embeddable groups.
Keywords
Cite
@article{arxiv.2409.16556,
title = {Twisted Roe algebras and their $K$-theory},
author = {Jintao Deng and Liang Guo},
journal= {arXiv preprint arXiv:2409.16556},
year = {2025}
}