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Groups which are not properly 3-realizable
Funar, Louis ; Lasheras, Francisco F. ; Repovš, Dušan, 1954-
A group is properly 3-realizable if it is the fundamental group of a compact polyhedron whose universal covering is proper homotopically equivalent to some3-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.
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