A proof of the simple connectivity at infinity of Out F4 Original Research Article

A finitely presented group G is said to be simply connected at infinity if, for any compact set C in the universal cover image for the standard 2-complex for G, there exists a compact set D such that any loop in image is homotopically trivial in image. Suppose that F4 is a free group on four generators, Aut F4 its automorphism group, and Inn F4 the subgroup of inner automorphisms. We use direct, elementary means to show that the outer automorphism group of rank 4, Aut F4/Inn F4 is simply connected at infinity.