On a quantitative operator K-theory
Operator Algebras
2012-04-17 v3 K-Theory and Homology
Metric Geometry
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.
Keywords
Cite
@article{arxiv.1106.2419,
title = {On a quantitative operator K-theory},
author = {Hervé Oyono-Oyono and Guoliang Yu},
journal= {arXiv preprint arXiv:1106.2419},
year = {2012}
}
Comments
some corrections and quantitative K-theory for Banach algebras has been outlined