On the Farrell-Jones conjecture for higher algebraic 𝐾-theory-Reference-Cited by-同舟云学术

On the Farrell-Jones conjecture for higher algebraic 𝐾-theory

Published:2005-03-30 Issue:3 Volume:18 Page:501-545
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Bartels Arthur,Reich Holger

Abstract

We prove the Farrell-Jones Conjecture for the algebraic K K -theory of a group ring R Γ R \Gamma in the case where the group Γ \Gamma is the fundamental group of a closed Riemannian manifold with strictly negative sectional curvature. The coefficient ring R R is an arbitrary associative ring with unit and the result applies to all dimensions.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/jams/2005-18-03/S0894-0347-05-00482-0/S0894-0347-05-00482-0.pdf

Reference39 articles.

1. Positive harmonic functions on complete manifolds of negative curvature;Anderson, Michael T.;Ann. of Math. (2),1985

2. Structure of manifolds of nonpositive curvature. I;Ballmann, Werner;Ann. of Math. (2),1985

3. Classifying space for proper actions and 𝐾-theory of group 𝐶*-algebras;Baum, Paul,1994

4. A foliated squeezing theorem for geometric modules;Bartels, Arthur,2003

Cited by 12 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The Bounded Isomorphism Conjecture for Box Spaces of Residually Finite Groups;Journal of Topology and Analysis;2023-06-20

2. Coassembly and the K-theory of finite groups;Advances in Mathematics;2017-02

3. Algebraic K-theory of group rings and the cyclotomic trace map;Advances in Mathematics;2017-01

4. On Proofs of the Farrell–Jones Conjecture;Topology and Geometric Group Theory;2016

5. The $K$-theoretic Farrell-Jones conjecture for CAT(0)-groups;Proceedings of the American Mathematical Society;2012-03-01