Homotopy ribbon discs with a fixed group

In the topological category, the classification of homotopy ribbon discs is known when the fundamental group G of the exterior is Z and the Baumslag-Solitar group BS.1; 2/.We prove that if a group G is geometrically 2-dimensional and satisfies the Farrell-Jones conjecture, then a condition involving the fundamental group ensures that exteriors of aspherical homotopy ribbon discs with fundamental group G are s-cobordant rel boundary.When G is good, this leads to the classification of such discs.As an application, for any knot J S 3 whose knot group G.J / is good, we classify the homotopy ribbon discs for J # J whose complement has group G.J /.A similar application is obtained for BS.m; n/ when jm nj D 1.