Enric Ventura, Universitat Politecnica de Catalunya

Abstract:
Recently, a (quite complicated) algorithm has been given to compute the fixed subgroup of an automorphism of a free group (the problem is quite delicate, for example, the corresponding problem for endomorphisms is open). In this talk we solve the two dual algorithmic problems: given a subgroup H of the free group, we can decide whether H is the fixed subgroup of a (finite) family of automorphisms, and whether it is the fixed subgroup of a (finite) family of endomorphisms. In particular, we'll see that these two problems are quite different.