Inheritance of Isomorphism Conjectures under colimits

Details Inheritance of Isomorphism Conjectures under colimits Inheritance of Isomorphism Conjectures under colimits

2007-02-15

arxiv.org/abs/math/0702460v2

Mathematics

K-Theory and Homology

30 pages This is the final version, minor changes only. It will appear in the Valladolid Conference on K-theory and Noncommuta

Scientific paper

We investigate when Isomorphism Conjectures, such as the ones due to Baum-Connes, Bost and Farrell-Jones, are stable under colimits of groups over directed sets (with not necessarily injective structure maps). We show in particular that both the K-theoretic Farrell-Jones Conjecture and the Bost Conjecture with coefficients hold for those groups for which Higson, Lafforgue and Skandalis have disproved the Baum-Connes Conjecture with coefficients.

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