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arXiv · 2409.16556

Twisted Roe algebras and their $K$-theory

Jintao Deng·Liang Guo
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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.

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Jintao Deng, Liang Guo. 2024-09-25. Twisted Roe algebras and their $K$-theory. https://arxiv.org/abs/2409.16556

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