On genus and cancellation in homotopy
type: Item
instance of: scholarly article
title: On genus and cancellation in homotopy
zbMATH Open document ID: 0744.55004
DOI: 10.1007/BF02773848
author: Imre Bokor
published in: Israel Journal of Mathematics
publication date: 1992-06-28T00:00:00Z
review text: The author proves the following Theorem. Suppose given \(\alpha_ i,\beta_ j\in\pi_{4n-1}(S^{2n})\), \(1\leq i\leq H\), \(1\leq j\leq H\), and assume that they are elements of infinite order for \(i\leq m\), \(j\leq m'\), and elements of finite order for \(i > m\), \(j > m'\). Denote by \(C_{\alpha_ i}\), \(C_{\beta_ j}\) the corresponding mapping cones. Then \(\bigvee^ H_{i=1}C_{\alpha_ i}\simeq \bigvee^ H_{j=1}C_{\beta_ j}\) if and only if: (i) \(m=m'\); (ii) \(C_{\alpha_ i}\simeq C_{\sigma(i)}\), \(i=1,\dots,m\), for some permutation \(\sigma\) of \(\{1,2,\dots,m\}\); (iii) \(\bigvee^ H_{i=m+1}C_{\alpha_ i}\simeq\bigvee^ H_{j=m+1}C_{\beta_ j}\).
reviewed by: Mamoru Mimura
Mathematics Subject Classification ID: 55P15
zbMATH DE Number: 32232
zbMATH Keywords: homotopy type of mapping cylinders
zbMATH Keywords: wedges of mapping cylinders
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 32232