Inheritance of Isomorphism Conjectures under colimits

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.

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

References in corpus (4)

• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• Lacunary hyperbolic groups
• Induction Theorems and Isomorphism Conjectures for K- and L-Theory
• On the Farrell-Jones Conjecture and its applications

Cited by in corpus (14)

• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• Algebraic K-theory of group rings and the cyclotomic trace map
• Survey on aspherical manifolds
• Survey on geometric group theory
• On crossed product rings with twisted involutions, their module categories and L-theory
• On the Farrell-Jones Conjecture and its applications
• A generalised Green-Julg theorem for proper groupoids and Banach algebras
• On the K-theory of subgroups of virtually connected Lie groups
• On the Farrell-Jones and related Conjectures
• Induction for Banach algebras, groupoids and KK^ban
• Non-connective K- and Nil-spectra of additive categorie
• Manifolds homotopy equivalent to certain torus bundles over lens spaces
• Topological Rigidity for FJ by the Infinite Cyclic Group
• A description of the assembly map for the Baum-Connes conjecture with coefficients