Enumerating limit groups (with H. Wilton). Preprint (2007). .pdf

Abstract We prove that the set of limit groups is recursive, answering a question of Delzant. One ingredient of the proof is the observation that a finitely presented group with local retractions (a la Long and Reid) is coherent and, furthermore, there exists an algorithm that computes presentations for finitely generated subgroups. The other main ingredient is the obility to algorithmically calculate centralizers in relatively hyperbolic gorups. Applications include the existence of a recognition algorithm for limit groups.