Article
Groups which are not properly 3-realizable
Author/s | Funar, Louis
Fernández Lasheras, Francisco Jesús Repovš, Dušan |
Department | Universidad de Sevilla. Departamento de Geometría y Topología |
Publication Date | 2012 |
Deposit Date | 2016-09-22 |
Published in |
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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 ... 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. |
Project ID. | 08677YJ
ANR-06-BLAN-0311 MTM 2010-20445 |
Citation | Funar, L., Fernández Lasheras, F.J. y Repovs, D. (2012). Groups which are not properly 3-realizable. Revista Matemática Iberoamericana, 28, 401-414. |
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