We prove that the set of limit groups is recursively enumerable, answering a question of Delzant. One ingredient of the proof is the observation that a finitely presented group with local retractions ((à 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 ability to algorithmically calculate centralizers in relatively hyperbolic groups. Applications include the existence of recognition algorithms for limit groups and free groups.
@article{10_4171_ggd_63,
author = {Daniel Groves and Henry Wilton},
title = {Enumerating limit groups},
journal = {Groups, geometry, and dynamics},
pages = {389--399},
year = {2009},
volume = {3},
number = {3},
doi = {10.4171/ggd/63},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/63/}
}
TY - JOUR
AU - Daniel Groves
AU - Henry Wilton
TI - Enumerating limit groups
JO - Groups, geometry, and dynamics
PY - 2009
SP - 389
EP - 399
VL - 3
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/63/
DO - 10.4171/ggd/63
ID - 10_4171_ggd_63
ER -
%0 Journal Article
%A Daniel Groves
%A Henry Wilton
%T Enumerating limit groups
%J Groups, geometry, and dynamics
%D 2009
%P 389-399
%V 3
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/63/
%R 10.4171/ggd/63
%F 10_4171_ggd_63
