Inheritance of Isomorphism Conjectures under colimits, by Arthur Bartels, Siegfried Echterhoff, and Wolfgang Lueck

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.

Arthur Bartels <>
Siegfried Echterhoff <>
Wolfgang Lueck <>