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Twisted Roe algebras and their $K$-theory

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arxiv 2409.16556 v2 pith:UUAJELN6 submitted 2024-09-25 math.KT math.FAmath.OA

Jintao Deng , Liang Guo This is my paper · ORCID
classification math.KTmath.FAmath.OA
keywords coarsetwistedbaum-connesconjecturecoefficientsalgebrasholdsmetric
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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. $K$-theory of ghostly ideals for $\ell^p$-coarsely embeddable spaces

    math.KT 2025-11 conditional novelty 7.0 of 10

    Bounded-geometry metric spaces coarsely embeddable into ℓ^p have the property that geometric ideals in their Roe algebras have the same K-theory as the corresponding ghostly ideals.

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