**
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.