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

Arthur Bartels·Wolfgang Lueck
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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.

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Arthur Bartels, Wolfgang Lueck. 2005-07-14. Isomorphism Conjecture for homotopy K-theory and groups acting on trees. https://arxiv.org/abs/math/0407489

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