The isomorphism conjecture for groups with generalized free product structure

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.

43 pages, Section 3 contains parts of arXiv:math/0510297. (to appear in the Handbook of Group Actions, Vol II.)

References in corpus (5)

• The Farrell-Jones isomorphism conjecture for 3-manifold groups
• The isomorphism conjecture for 3-manifold groups and K-theory of virtually poly-surface groups
• On the isomorphism conjecture for groups acting on trees
• The isomorphism conjecture in L-theory: graphs of groups
• Surgery groups of the fundamental groups of hyperplane arrangement complements

Cited by in corpus (1)

• Configuration Lie groupoids and orbifold braid groups