On a quantitative operator K-theory

Details On a quantitative operator K-theory On a quantitative operator K-theory

2011-06-13

arxiv.org/abs/1106.2419v3

Mathematics

Operator Algebras

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

Scientific paper

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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