| On the Proper Homotopy Invariance of the Tucker Property |
| |
| 引用本文： | Daniele Ettore OTERA. On the Proper Homotopy Invariance of the Tucker Property[J]. 数学学报(英文版), 2007, 23(3): 571-576. DOI: 10.1007/s10114-005-0900-2 |
| |
| 作者姓名： | Daniele Ettore OTERA |
| |
| 作者单位： | [1]Universitd di Palermo, Dipartimento di Matematica ed Applicazioni, via Archirafi 34, 90123 - Palermo, Italy [2]Universitd Paris-Sud, Mathdmatiques, Bdt 425, 91405 Orsay Cedex - France |
| |
| 基金项目： | The author is partially supported by GNSAGA of INDAM, by MIUR of Italy （Progetto Giovani Ricercatori） and by Universith di Palermo Acknowledgments The author is indebted to Valentin Poenaru and Louis Funar for useful discussions, comments and suggestions. Part of this work was done when the author visited the Institut Fourier of Grenoble, which he wishes to thank for their support and hospitality. |
| |
| 摘 要： | A non-compact polyhedron P is Tucker if, for any compact subset K begong to P, the fundamental group π1 （P - K） is finitely generated. The main result of this note is that a manifold which is proper homotopy equivalent to a Tucker polyhedron is Tucker. We use Poenaru＇s theory of the equivalence relations forced by the singularities of a non-degenerate simplicial map.
|
| 关 键 词： | 真同伦 不变性 Tucker性质 非紧多面体 |
| 收稿时间： | 2005-09-16 |
| 修稿时间： | 2005-09-162006-03-01 |
On the Proper Homotopy Invariance of the Tucker Property |
| |
| Daniele Ettore Otera. On the Proper Homotopy Invariance of the Tucker Property[J]. Acta Mathematica Sinica(English Series), 2007, 23(3): 571-576. DOI: 10.1007/s10114-005-0900-2 |
| |
| Authors: | Daniele Ettore Otera |
| |
| Affiliation: | (1) Universitá di Palermo, Dipartimento di Matematica ed Applicazioni, via Archirafi 34, 90123 Palermo, Italy;(2) Université Paris-Sud, Mathématiques, Bat 425, 91405 Orsay Cedex, France |
| |
| Abstract: | A non-compact polyhedron P is Tucker if, for any compact subset K ⊂ P, the fundamental group π 1(P − K) is finitely generated. The main result of this note is that a manifold which is proper homotopy equivalent to a Tucker polyhedron is Tucker. We use Poenaru’s theory of the equivalence relations forced by the singularities of a non-degenerate simplicial map. The author is partially supported by GNSAGA of INDAM, by MIUR of Italy (Progetto Giovani Ricercatori) and by Università di Palermo |
| |
| Keywords: | proper homotopy Φ /Ψ -theory tucker property |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
