Finding infinity inside Outer space

9 May 2016
Karen Vogtmann

Motivated by work of Borel and Serre on arithmetic groups, Bestvina and Feighn defined a bordification of Outer space; this is an enlargement of Outer space which is highly-connected at infinity and on which the action of $Out(F_n)$ extends, with compact quotient. They conclude that $Out(F_n)$ satisfies a type of duality between homology and cohomology.  We show that Bestvina and Feighn’s  bordification can be realized as a deformation retract of Outer space instead of an extension, answering some questions left open by Bestvina and Feighn and considerably simplifying their proof that the bordification is highly connected at infinity.