A Borsuk-Ulam type theorem for sphere bundles over stunted projective spaces
type: Item
instance of: scholarly article
title: A Borsuk-Ulam type theorem for sphere bundles over stunted projective spaces
zbMATH Open document ID: 1170.55002
author: Ryuichi Tanaka
published in: Topology and its Applications
publication date: 2009-04-03T00:00:00Z
review text: A \(CW\)-complex \(B\) is I-trivial if there does not exist a \(\mathbb Z_2\)-map from \( S^{i-1}\) to \(S(\alpha)\) for any vector bundle \(\alpha\) over \(B\) and any integer \(i\), with \(i>\dim(\alpha)\). In this paper the author studies whether or not the stunted projective space \(FP_m^{n}= \frac{FP^n}{FP^{m-1}}\), \(1\leq m \leq n\) is I-trivial. So, \(FP_{m}^{n} \) is not I-trivial in the case \(m=1\) while it is I-trivial in the case where \(m=n\) and, for \(d=\dim_{\mathbb R}F\), \(dn \neq 1,2,4,8\) . A space \(B\) is \(W\)-trivial if \(W(\alpha)=1\) holds for every vector bundle \(\alpha\) over \(B\) (where \(W(\alpha)\) denotes the total Stiefel-Whitney class of \(\alpha\)).
reviewed by: Corina Mohorianu
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 55R25
zbMATH DE Number: 5539517
zbMATH Keywords: sphere bundle
zbMATH Keywords: \(\mathbb Z_2\)-map
zbMATH Keywords: index
zbMATH Keywords: equivariant homotopy theory
MaRDI profile type: Publication
full work available at URL: j.topol.2008.11.011
OpenAlex ID: W2045136894
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DOI: 10.1016/J.TOPOL.2008.11.011
description: scientific article; zbMATH DE number 5539517