Article
One-relator groups and proper 3-realizability
Author/s | Cárdenas Escudero, Manuel Enrique
Fernández Lasheras, Francisco Jesús Quintero Toscano, Antonio Rafael Repovš, Dušan |
Department | Universidad de Sevilla. Departamento de Geometría y Topología |
Publication Date | 2009 |
Deposit Date | 2016-07-08 |
Published in |
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Abstract | How different is the universal cover of a given finite 2-complex from a 3-manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group G is said to be properly 3-realizable ... How different is the universal cover of a given finite 2-complex from a 3-manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group G is said to be properly 3-realizable if there exists a compact 2-polyhedron K with π1(K) ∼= G whose universal cover K˜ has the proper homotopy type of a PL 3-manifold (with boundary). In this paper, we study the asymptotic behavior of finitely generated one-relator groups and show that those having finitely many ends are properly 3-realizable, by describing what the fundamental pro-group looks like, showing a property of one-relator groups which is stronger than the QSF property of Brick (from the proper homotopy viewpoint) and giving an alternative proof of the fact that one-relator groups are semistable at infinity. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España |
Project ID. | MTM 2007-65726
BI-ES/04-05-014 |
Citation | Cárdenas Escudero, M.E., Fernández Lasheras, F.J., Quintero Toscano, A.R. y Repovš, D. (2009). One-relator groups and proper 3-realizability. Revista Matemática Iberoamericana, 25, 739-756. |
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