Given an endomorphism h of a free group F, the fixed subgroup of h consists of those elements x ∈ F for which h(x)=x. In this talk I will give some background on fixed subgroups in free groups, and then present an algorithm which computes the fixed subgroup and the stable image for any endomorphism of the free group of rank 2. This answers, for rank 2, a question posed by Stallings in 1984 and a more recent question of Ventura. I will explain why general endomorphisms are more difficult than automorphisms, and in what ways our algorithm needs the restriction on the rank. This is joint work with Alan Logan.
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
