The suspension order of the real even dimensional projective space
type: Item
instance of: scholarly article
title: The suspension order of the real even dimensional projective space
zbMATH Open document ID: 1063.55005
author: Juno Mukai
published in: Journal of Mathematics of Kyoto University
publication date: 2005-01-03T00:00:00Z
review text: In the category of pointed topological spaces, denote the suspension of \(X\) by \(\Sigma X\), and the identity class of \(X\) by \(\iota_X\). The order of \(\iota_{\Sigma X}\in [\Sigma X,\Sigma X]\) is called the suspension order (or the characteristic) of \(X\). The order of \(\Sigma^{\infty}\iota_X\) is called the stable order of \(X\) [see \textit{H. Toda}, Ann. Math. 78, 300--325 (1963; Zbl 0146.18901)]. Let P\(^{n}\) be the real projective space of dimension \(n\). The main theorem in this paper states that the suspension order of P\(^6\) is \(8\). As an application of the theorem, the author concludes the truth of the conjecture in [\textit{J. Mukai}, J. Math. Soc. Japan 40, 53--63 (1988; Zbl 0637.55008)]: The suspension order of P\(^{2n}\) coincides with its stable order.
Mathematics Subject Classification ID: 55P05
Mathematics Subject Classification ID: 55Q15
Mathematics Subject Classification ID: 55Q52
zbMATH DE Number: 2124477
zbMATH Keywords: projective space
zbMATH Keywords: suspension
zbMATH Keywords: suspension order
zbMATH Keywords: stable
reviewed by: J. Remedios
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250281734
OpenAlex ID: W1586790826
DOI: 10.1215/KJM/1250281734
description: scientific article; zbMATH DE number 2124477