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Inheritance of Isomorphism Conjectures under colimits

Arthur Bartels·Siegfried Echterhoff·Wolfgang Lueck
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Abstract

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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Arthur Bartels, Siegfried Echterhoff, Wolfgang Lueck. 2007-05-09. Inheritance of Isomorphism Conjectures under colimits. https://arxiv.org/abs/math/0702460

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