A Whitehead algorithm for toral relatively hyperbolic groups

Abstract

The Whitehead problem is solved in the class of toral relatively hyperbolic groups $ G$ (i.e. torsion-free relatively hyperbolic groups with abelian parabolic subgroups): there is an algorithm which, given two finite tuples $ (u_1, \ldots ,u_n)$ and $ (v_1, \ldots ,v_n)$ of elements of $ G$ , decides whether there is an automorphism of $ G$ taking $ u_i$ to $ v_i$ for all $ i$ .