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

2004/07/28 by Arthur Bartels, Bartels, Arthur, Wolfgang Lueck +1
Mathematics · #19D35 #19D55 #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT #msc:19D35 #msc:19D55

paper · pdf · doi:10.48550/arxiv.math/0407489

40 pages, to appear in J. Pure Applied Algebra

arxiv created 2005/07/14 · arxiv updated 2009/12/01

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.

Related

• On the isomorphism conjecture for groups acting on trees
• The Farrell-Jones Isomorphism Conjecture in K-Theory
• Trees are 1-Transfer
• A Dirac Morphism for the Farrell-Jones Isomorphism Conjecture in K-Theory
• A Controlled Approach to the Isomorphism Conjecture