Isomorphism Conjecture for homotopy K-theory and groups acting on trees
By Arthur Bartels, W. Lück. 2004
57 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6fc26b6ec26bad434dac296691952aedd0ac4f37
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In Geometry and Topology
- W. Lück
- Arthur Bartels
- H. Reich
- Michael Weiermann
- Christian Wegner
- Hanfeng Li
- Michael W. Davis
- Damien Gaboriau
In Mathematical Physics
- W. Lück
- Arthur Bartels
- H. Reich
- Michael Weiermann
- Christian Wegner
- Hanfeng Li
- Michael W. Davis
- Holger Kammeyer
Citations in the corpus
- Coefficients for the Farrell¿Jones Conjecture (2005, background): “J93, Section 1.7] can be formulated as follows: for every group homeomorphism Φ: K→ Gthe assembly map HK ∗ (EΦ∗VCycK;K R) → HK∗(pt;K ) is an isomorphism, see Section 6 and in particular Remark 6.6 in [BL04]. Therefore by Corollary 4.3 the Farrell-Jones Conjecture with Coefficients 3.2 implies the Fibe”
- On the classifying space of the family of virtually cyclic subgroups (2007, background): “If V is of type II, then it can be written as an amalgamated product V1 ∗V0 V2 of finite groups, where V0 has index two in both V1 and V2. In this case, HV ∗ (EV → {•};KR) is the non-connective version of Waldhausen’s Nil-term associated to this amalgamated product (see [ 1, Section 9 ]).”