Immutability is not uniformly decidable in hyperbolic groups (with H. Wilton. Preprint (2017). .pdf

Abstract A finitely generated subgroup H of a torsion-free hyperbolic group G is called immutable if there are only finitely many conjugacy classes of injections of H into G. We show that there is no uniform algorithm to recognize immutability, answering a uniform version asked by the authors.