# Trees are 1-Transfer

## TL;DR

This paper constructs an explicit 1-transfer space to advance the understanding of the Farrell-Jones conjecture for hyperbolic groups, leveraging geometric group properties.

## Contribution

It provides a concrete construction of a 1-transfer space, enhancing tools for proving the Farrell-Jones conjecture for hyperbolic groups.

## Key findings

- Explicit 1-transfer space construction for hyperbolic groups
- Improved techniques for Farrell-Jones conjecture proofs
- Enhanced understanding of geometric properties in group theory

## 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.