Groups which are not properly 3-realizable
Geometric Topology
2016-04-08 v3 Group Theory
Abstract
A group is properly 3-realizable if it is the fundamental group of a compact polyhedron whose universal covering is proper homotopically equivalent to some 3-manifold. We prove that when such a group is also quasi-simply filtered then it has {\em pro-(finitely generated free) fundamental group at infinity} and {\em semi-stable ends}. Conjecturally the quasi-simply filtration assumption is superfluous. Using these restrictions we provide the first examples of finitely presented groups which are not properly 3-realizable, for instance large families of Coxeter groups.
Keywords
Cite
@article{arxiv.0709.1576,
title = {Groups which are not properly 3-realizable},
author = {Louis Funar and Francisco F. Lasheras and Dusan Repovs},
journal= {arXiv preprint arXiv:0709.1576},
year = {2016}
}
Comments
revised version, 16p