Isomorphism Conjecture for homotopy K-theory and groups acting on trees

Abstract

We discuss an analogon to the Farrell-Jones Conjecture for homotopy algebraic K-theory. In particular, we prove that if a group G acts on a tree and all isotropy groups satisfy this conjecture, then G satisfies this conjecture. This result can be used to get rational injectivity results for the assembly map in the Farrell-Jones Conjecture in algebraic K-theory.

40 pages, to appear in J. Pure Applied Algebra

References in corpus (3)

• On the Farrell-Jones Conjecture for higher algebraic K-theory
• Induction Theorems and Isomorphism Conjectures for K- and L-Theory
• A Controlled Approach to the Isomorphism Conjecture

Cited by in corpus (1)

• Induction Theorems and Isomorphism Conjectures for K- and L-Theory