Twisted Roe algebras and their K-theory

2024/09/25 by Jintao Deng, Deng, Jintao, Guo Liang +1 · 1 citation
Mathematics · #19K56 #47L30 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2409.16556

openalex publication_date 2024/09/25 · openalex created_date 2024/10/26 · openalex updated_date 2026/07/28

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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• K-theory of ghostly ideals for ℓ^p-coarsely embeddable spaces

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