Farrell-Jones via Dehn fillings

Abstract

Following the approach of Dahmani, Guirardel and Osin, we extend the group theoretical Dehn filling theorem to show that the pre-images of infinite order elements have a certain structure of a free product. We then apply this result to show that groups hyperbolic relative to residually finite groups satisfying the Farrell-Jones conjecture, they satisfy the Farrell-Jones conjecture.

19 pages

References in corpus (2)

• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• Coarse flow spaces for relatively hyperbolic groups

Cited by in corpus (1)

• Cohomology of group theoretic Dehn fillings I: Cohen-Lyndon type theorems