On a quantitative operator K-theory

2011/06/13 by Hervé Oyono‐Oyono, Hervé Oyono-Oyono, Guoliang Yu +2 · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #math.KT #math.MG #math.OA

paper · pdf · doi:10.48550/arxiv.1106.2419

some corrections and quantitative K-theory for Banach algebras has been outlined

arxiv created 2012/04/14 · arxiv updated 2012/04/17

Abstract

In this paper, we develop a quantitative K-theory for filtered C*-algebras. Particularly interesting examples of filtered C*-algebras include group C*-algebras, crossed product C*-algebras and Roe algebras. We prove a quantitative version of the six term exact sequence and a quantitative Bott periodicity. We apply the quantitative K-theory to formulate a quantitative version of the Baum-Connes conjecture and prove that the quantitative Baum-Connes conjecture holds for a large class of groups.

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