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On the quantitative coarse Baum-Connes conjecture with coefficients

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arxiv 2410.11929 v1 pith:SZJL2YHV submitted 2024-10-15 math.OA math.KT

Jianguo Zhang This is my paper · ORCID
classification math.OAmath.KT
keywords baum-connescoarseconjecturecoefficientsqcbcquantitativemetricspaces
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In this paper, we introduce the quantitative coarse Baum-Connes conjecture with coefficients (or QCBC, for short) for proper metric spaces which refines the coarse Baum-Connes conjecture. And we prove that QCBC is derived by the coarse Baum-Connes conjecture with coefficients which provides many examples satisfying QCBC. In the end, we show QCBC can be reduced to the uniformly quantitative coarse Baum-Connes conjecture with coefficients of a sequence of bounded metric spaces.

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Cited by 1 Pith paper

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  1. The Baum-Connes and the Mishchenko-Kasparov assembly maps for group extensions

    math.OA 2026-01 conditional novelty 7.0 of 10

    For group extensions, injectivity, surjectivity and isomorphism of the Baum-Connes assembly map, and rational injectivity of the Mishchenko-Kasparov map, pass from quotient and fiber pieces to the whole group under ex...

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