Endomorphisms of free groups and their fixed points

Abstract

Much work recently has been focused on the issue of fixed words for automorphisms of free groups - see [2] and papers referred to there. Bestvina and Handel [1] have announced a powerful structure theorem for automorphisms of free groups that has as a consequence a proof of what has become known, to the amusement of Peter Scott, as the ‘so-called’ Scott Conjecture: if F is a free group of rank n and α:F→F is an automorphism, then Fix (α) = {w∈F|α(w) = w} has rank at most n.