A note on the Farrell-Jones conjecture for relatively hyperbolic groups

Abstract

For a group G relatively hyperbolic to a family of residually finite groups satisfying the Farrell-Jones conjecture, we reduce the solution of the Farrell-Jones conjecture for G to the case of certain nice cyclic extensions in G.

The proof of Theorem 1.1 in the previous version contained a mistake. Theorem 1.1 replaced by Proposition 3.2 which is a weaker result