Trees are 1-Transfer

Abstract

The K-theoretic Farrell-Jones isomorphism conjecture for a group ring $R[G]$ has been proved for several groups. The toolbox for proving the Farrell-Jones conjecture for a given group depends on some geometric properties of the group as it is the case of hyperbolic groups. The technique used to prove it for hyperbolic groups $G$ relies in the concept of an $N$-transfer space endowed with a $G$ action. In this work, we give an explicit construction of a $1$-transfer space.