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.
Cite this article
Laurent Bartholdi, (Self-)similar groups and the Farrell–Jones conjectures. Groups Geom. Dyn. 7 (2013), no. 1, pp. 1–11DOI 10.4171/GGD/175