Compact operators and algebraic $K$-theory for groups which act properly and isometrically on Hilbert space
K-Theory and Homology
2014-12-16 v5 Algebraic Topology
Group Theory
Operator Algebras
Abstract
We prove the -theoretic Farrell-Jones conjecture for groups as in the title with coefficient rings and -algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture with coefficients holds for such groups, to show that if is as in the title then the algebraic and the -crossed products of with a stable -algebra have the same -theory.
Keywords
Cite
@article{arxiv.1311.6285,
title = {Compact operators and algebraic $K$-theory for groups which act properly and isometrically on Hilbert space},
author = {Guillermo Cortiñas and Gisela Tartaglia},
journal= {arXiv preprint arXiv:1311.6285},
year = {2014}
}
Comments
Final version, to appear in Journal f\"ur die reine und angewandte Mathematik