We define a "nice representation" of a finitely presented group Γ as being a non-degenerate essentially surjective simplicial map f from a „nice" space X into a 3-complex associated to a presentation of Γ, with a strong control over the singularities of f, and such that X is WGSC (weakly geometrically simply connected), meaning that it admits a filtration by simply connected and compact subcomplexes. In this paper we study such representations for a very large class of groups, namely QSF (quasi-simply filtered) groups, where QSF is a topological tameness condition of groups that is similar to, but weaker than, WGSC. In particular, we prove that any QSF group admits a WGSC representation which is locally finite, equivariant and whose double point set is closed.
1
Vilnius University, Lithuania
2
Université Paris-Sud 11, France
Daniele Ettore Otera; Valentin Poénaru. Finitely presented groups and the Whitehead nightmare. Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 291-310. doi: 10.4171/ggd/397
@article{10_4171_ggd_397,
author = {Daniele Ettore Otera and Valentin Po\'enaru},
title = {Finitely presented groups and the {Whitehead} nightmare},
journal = {Groups, geometry, and dynamics},
pages = {291--310},
year = {2017},
volume = {11},
number = {1},
doi = {10.4171/ggd/397},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/397/}
}
TY - JOUR
AU - Daniele Ettore Otera
AU - Valentin Poénaru
TI - Finitely presented groups and the Whitehead nightmare
JO - Groups, geometry, and dynamics
PY - 2017
SP - 291
EP - 310
VL - 11
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/397/
DO - 10.4171/ggd/397
ID - 10_4171_ggd_397
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%A Valentin Poénaru
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%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/397/
%R 10.4171/ggd/397
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