Polyhedra with finite fundamental group dominate finitely many different homotopy types

被引：8
作者：
Kolodziejczyk, D [1 ]
机构：
[1] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00661 Warsaw, Poland
来源：
FUNDAMENTA MATHEMATICAE | 2003年 / 180卷 / 01期
关键词：
polyhedron; CW-complex; homotopy type; homotopy domination; shape; shape domination;
D O I：
10.4064/fm180-1-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In 1968 K. Borsuk asked: Does every polyhedron dominate only finitely many different shapes? In this question the notion of shape can be replaced by the notion of homotopy type. We showed earlier that the answer to the Borsuk question is no. However, in a previous paper we proved that every simply connected polyhedron dominates only finitely many different homotopy types (equivalently, shapes). Here we prove that the same is true for polyhedra with finite fundamental group.
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页码：1 / 9
页数：9
相关论文
共 22 条
[1]  
BORSUK K, 1975, STUDIES TOPOLOGY, P67
[2]  
Borsuk K., 1975, Theory of Shape
[3]  
Dydak J., 1980, Fundam. Math, V107, P58
[4]  
DYDAK J, 1978, LECT NOTES MATH, V688, DOI DOI 10.1007/BFB0101779
[5]   HOMOTOPY IDEMPOTENTS ON FINITE-DIMENSIONAL COMPLEXES SPLIT [J].
HASTINGS, HM ;
HELLER, A .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 85 (04) :619-622
[6]  
Hilton P., 1975, Localization of nilpotent groups and spaces, V15
[7]  
Hilton P.J., 1961, INTRO HOMOTOPY THEOR
[8]  
HOLSZTYNSKI W, 1971, MICH MATH J, V18, P409
[9]   Homotopy dominations within polyhedra [J].
Kolodziejczyk, D .
FUNDAMENTA MATHEMATICAE, 2003, 178 (03) :189-202
[10]  
Kolodziejczyk D, 1996, FUND MATH, V151, P39
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