Article
Relating the Freiheitssatz to the asymptotic behavior of a group
Author/s | Fernández Lasheras, Francisco Jesús
Roy, Ranja |
Department | Universidad de Sevilla. Departamento de Geometría y Topología |
Publication Date | 2013 |
Deposit Date | 2016-10-04 |
Published in |
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Abstract | We are concerned with the implications of the Freiheitssatz
property for certain group presentations in terms of proper homotopy invariants of the underlying group, by describing its fundamental pro-group.
A finitely ... We are concerned with the implications of the Freiheitssatz property for certain group presentations in terms of proper homotopy invariants of the underlying group, by describing its fundamental pro-group. A finitely presented group G is said to be properly 3-realizable if it is the fundamental group of a finite 2-dimensional CW-complex whose universal cover has the proper homotopy type of a 3-manifold. We show that if an infinite finitely presented group G is given by some special kind of presentation satisfying the Freiheitssatz, then G is semistable at infinity and properly 3-realizable. In particular, this applies to groups given by a staggered presentation. |
Funding agencies | Ministerio de Ciencia e Innovación (MICIN). España |
Project ID. | MTM2010-20445 |
Citation | Fernández Lasheras, F.J. y Roy, R. (2013). Relating the Freiheitssatz to the asymptotic behavior of a group. Revista Matemática Iberoamericana, 29 (1), 75-89. |
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