On the Lusternik-Schnirelmann category of Stiefel manifolds
type: Item
instance of: scholarly article
title: On the Lusternik-Schnirelmann category of Stiefel manifolds
zbMATH Open document ID: 1124.55003
author: Tetsu Nishimoto
published in: Topology and its Applications
publication date: 2007-05-30T00:00:00Z
review text: Following the computational method initiated by W. Singhof, the author determines the Lusternik-Schnirelmann category of the real Stiefel manifold \(V_{n,k}\) and of the quaternionic Stiefel manifold \(X_{n,k}\). More precisely, he proves that for \(n\geq 2k\) the Lusternik-Schnirelmann category of \(V_{n,k}\) (respectively of \(X_{n,k}\)) equals the cup-length of \(H^*(V_{n,k};\mathbb{F}_2)\) (respectively, of \(H^*(X_{n,k};\mathbb{Z}))\).
Mathematics Subject Classification ID: 55M30
zbMATH DE Number: 5159481
zbMATH Keywords: Lusternik-Schnirelmann category
zbMATH Keywords: cellular decomposition
zbMATH Keywords: Stiefel manifold
reviewed by: Jean-Claude Thomas
MaRDI profile type: Publication
full work available at URL: j.topol.2007.02.002
OpenAlex ID: W2037601269
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cites work: Q5328638
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DOI: 10.1016/J.TOPOL.2007.02.002
description: scientific article; zbMATH DE number 5159481