A proof of the simple connectivity at infinity of Out F-4

A finitely presented group G is said to be simply connected at infinity if, for any compact set C in the universal cover (X) over tilde for the standa rd 2-complex for G, there exists a compact set D such that any loop in (X) over tilde\D is homotopically trivial in (X) over tilde\C. Suppose that F-4 is a free group on four generators, Aut F-4 its automorphism group, and In n F-4 the subgroup of inner automorphisms. We use direct, elementary means to show that the outer automorphism group of rank 4, Ant F-4/Inn F-4 is sim ply connected at infinity. (C) 2000 Elsevier Science B.V. All rights reserv ed.