Simply-connected polyhedra dominate only finitely many different shapes

被引：6

作者：

Kolodziejczyk, D

机构：

[1] Polish Acad Sci, Inst Math, PL-00950 Warsaw, Poland

[2] Warsaw Univ Technol, PL-00661 Warsaw, Poland

来源：

TOPOLOGY AND ITS APPLICATIONS | 2001年 / 112卷 / 03期

关键词：

shape; homotopy type; polyhedron; CW-complex; shape domination; homotopy domination; simply-connected;

D O I：

10.1016/S0166-8641(00)00004-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1968 ii. Borsuk asked: Is it true that every finite polyhedron dominates only finitely many different shapes? In some previous paper we have shown that an answer to this question is negative. However, using the localization in homotopy theory we obtain that every simply-connected polyhedron dominates only finitely many different shapes. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：289 / 295

页数：7

共 5 条

[1] Polyhedra with finite fundamental group dominate finitely many different homotopy types
Kolodziejczyk, D
FUNDAMENTA MATHEMATICAE, 2003, 180 (01) : 1 - 9
[2] CHARACTERIZATIONS OF SIMPLY-CONNECTED FINITE POLYHEDRA IN 3-SPACE
KONG, TY
ROSCOE, AW
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1985, 17 (NOV) : 575 - 578
[3] On open 3-manifolds proper homotopy equivalent to geometrically simply-connected polyhedra
Funar, L
Thickstun, TL
TOPOLOGY AND ITS APPLICATIONS, 2001, 109 (02) : 191 - 200
[4] Polyhedra dominating finitely many different homotopy types
Kolodziejczyk, D
TOPOLOGY AND ITS APPLICATIONS, 2005, 146 : 583 - 592
[5] Infinite connected components of an Auslander-Reiten quiver in which each DTr-orbit contains only finitely many points
Yao, HL
COMMUNICATIONS IN ALGEBRA, 1999, 27 (11) : 5167 - 5189

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