The isomorphism conjecture for groups with generalized free product structure
Geometric Topology
2016-01-25 v1 Algebraic Topology
K-Theory and Homology
Abstract
In this article we study the K- and L-theory of groups acting on trees. We consider the problem in the context of the fibered isomorphism conjecture of Farrell and Jones. We show that in the class of residually finite groups it is enough to prove the conjecture for finitely presented groups with one end. Also, we deduce that the conjecture is true for the fundamental groups of graphs of finite groups and of trees of virtually cyclic groups. To motivate the reader we include a survey on some classical works on this subject.
Cite
@article{arxiv.1410.7937,
title = {The isomorphism conjecture for groups with generalized free product structure},
author = {S. K. Roushon},
journal= {arXiv preprint arXiv:1410.7937},
year = {2016}
}
Comments
43 pages, Section 3 contains parts of arXiv:math/0510297. (to appear in the Handbook of Group Actions, Vol II.)