Are Two Given Maps Homotopic? An Algorithmic Viewpoint

被引:0
作者
M. Filakovský
L. Vokřínek
机构
[1] IST Austria,
[2] Masaryk University,undefined
来源
Foundations of Computational Mathematics | 2020年 / 20卷
关键词
Homotopy; Suspension; Polycyclic group; Algorithm; 55Q05; 55P40;
D O I
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中图分类号
学科分类号
摘要
This paper presents two algorithms. The first decides the existence of a pointed homotopy between given simplicial maps f,g:X→Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f {},\,g:X\rightarrow Y$$\end{document}, and the second computes the group [ΣX,Y]∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[\varSigma X,Y]^*$$\end{document} of pointed homotopy classes of maps from a suspension; in both cases, the target Y is assumed simply connected. More generally, these algorithms work relative to A⊆X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A\subseteq X$$\end{document}.
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页码:311 / 330
页数:19
相关论文
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[4]  
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[5]  
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