Revista Matemática Iberoamericana

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Volume 28, Issue 2, 2012, pp. 401–414
DOI: 10.4171/rmi/682

Published online: 2012-04-22

Groups which are not properly 3-realizable

Louis Funar[1], Francisco F. Lasheras[2] and Dušan Repovš[3]

(1) Université Grenoble I, Saint-Martin-d'Hères, France
(2) Universidad de Sevilla, Spain
(3) University of Ljubljana, Slovenia

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 pro-(finitely generated free) fundamental group at infinity and 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: Properly 3-realizable, geometric simple connectivity, quasi-simple filtered group, Coxeter group

Funar Louis, Lasheras Francisco, Repovš Dušan: Groups which are not properly 3-realizable. Rev. Mat. Iberoamericana 28 (2012), 401-414. doi: 10.4171/rmi/682