A proof of the simple connectivity at infinity of OutF4

Abstract

A finitely presented group G is said to be simply connected at infinity if, for any compact set C in the universal cover X̃ for the standard 2-complex for G, there exists a compact set D such that any loop in X ̃ ⧹D is homotopically trivial in X ̃ ⧹C . Suppose that F 4 is a free group on four generators, Aut F 4 its automorphism group, and Inn F 4 the subgroup of inner automorphisms. We use direct, elementary means to show that the outer automorphism group of rank 4, Aut F 4/Inn F 4 is simply connected at infinity.