Groups, Geometry, and Dynamics

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Volume 7, Issue 1, 2013, pp. 1–11
DOI: 10.4171/GGD/175

Published online: 2013-01-31

(Self-)similar groups and the Farrell–Jones conjectures

Laurent Bartholdi[1]

(1) Georg-August-Universität Göttingen, Germany

We show that contracting self-similar groups satisfy the Farrel–Jones conjectures as soon as their universal contracting cover is non-positively curved. This applies in particular to bounded self-similar groups.

We define, along the way, a general notion of contraction for groups acting on a rooted tree in a not necessarily self-similar manner.

Keywords: Self-similar bounded group, K-theory

Bartholdi Laurent: (Self-)similar groups and the Farrell–Jones conjectures. Groups Geom. Dyn. 7 (2013), 1-11. doi: 10.4171/GGD/175