The Automorphic Conjugacy Problem for Subgroups of Fundamental Groups of Compact Surfaces

Abstract

Let Σ be a compact connected surface with basepoint x and H1 and H2 be two finitely generated subgroups of π1(Σ, x) on finite sets of generators. It is proved that there exists an algorithm which decides whether there is an automorphism \(\alpha \in {Aut(\pi }_{1} {(}\sum {,}\;x{))}\) for which α (H1) = H2, and if so, it finds such.