Groups which are not properly 3-realizable

Louis Funar; Francisco F. Lasheras; Dusan Repovs

doi:10.4171/rmi/682

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arXiv · 0709.1576

Groups which are not properly 3-realizable

Louis Funar·Francisco F. Lasheras·Dusan Repovs

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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.

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BibTeX RIS

Louis Funar, Francisco F. Lasheras, Dusan Repovs. 2007-09-11. Groups which are not properly 3-realizable. https://doi.org/10.4171/rmi/682

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