English

Inheritance of Isomorphism Conjectures under colimits

K-Theory and Homology 2007-05-23 v2

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.

Keywords

Cite

@article{arxiv.math/0702460,
  title  = {Inheritance of Isomorphism Conjectures under colimits},
  author = {Arthur Bartels and Siegfried Echterhoff and Wolfgang Lueck},
  journal= {arXiv preprint arXiv:math/0702460},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T17:51:09.632Z