On the bordification of outer space

TL;DR

This paper presents a simplified construction of the Bestvina-Feighn bordification of Outer space, leading to easier proofs of its connectivity properties and implications for the group Out(F_n).

Contribution

It introduces a straightforward equivariant deformation retract of Outer space that is homeomorphic to the bordification, simplifying previous proofs.

Findings

The bordification is (2n-5)-connected at infinity.

Out(F_n) is a virtual duality group.

Simplified proof of the bordification's connectivity properties.

Abstract

We give a simple construction of an equivariant deformation retract of Outer space which is homeomorphic to the Bestvina-Feighn bordification. This results in a much easier proof that the bordification is (2n-5)-connected at infinity, and hence that $Out(F_n)$ is a virtual duality group.