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

Abstract

We show that contracting self-similar groups satisfy the Farrell-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.

9 pages; new version corrects terminology and an erroneous claim about zero divisors

References in corpus (4)

• Post-critically finite self-similar groups
• On crossed product rings with twisted involutions, their module categories and L-theory
• The K-theoretic Farrell-Jones conjecture for CAT(0)-groups
• The Farrell-Jones Conjecture for cocompact lattices in virtually connected Lie groups

Cited by in corpus (1)

• Amenable groups without finitely presented amenable covers