Morse-Bott functions and the Lusternik-Schnirelmann category
type: Item
instance of: scholarly article
title: Morse-Bott functions and the Lusternik-Schnirelmann category
zbMATH Open document ID: 1233.55004
author: Hiroyuki Kadzisa
author: Mamoru Mimura
published in: Journal of Fixed Point Theory and Applications
publication date: 2011-11-04T00:00:00Z
review text: The authors construct cone-decompositions of manifolds by using \(C^1\)-differentiable functions and their gradient flows and they use these decompositions to obtain an upper bound for the Lusternik-Schnirelmann category. The main result of the paper is stated in Theorem 1.3 and it is proved in Section 4. In particular, the Morse-Bott functions on the Stiefel manifolds considered by \textit{T. Frankel} in [\textit{S. Cairns} (ed.), Differential and combinatorial topology. A symposium in honor of Marston Morse. Princeton, N.J.: Princeton University Press. (1965; Zbl 0127.24202), pp. 37--53] are used to construct the cone-decompositions of Stiefel manifolds and of symmetric Riemannian spaces in order to determine their Lusternik-Schnirelmann category. Most of the presented results are connected to earlier papers by the authors, e.g. [the authors, Topology Appl. 156, No. 2, 348--364 (2008; Zbl 1157.57024), \textit{H. Kadzisa}, Topology Appl. 153, No. 9, 1383--1398 (2006; Zbl 1089.55003) and \textit{M. Mamoru} and \textit{N. Iwase}, in: G. Arone (ed.) et al., Categorical decomposition techniques in algebraic topology. Basel: Birkhäuser. Prog. Math. 215, 199--212 (2004; Zbl 1050.55002)].
reviewed by: Dorin Andrica
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 22F30
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 5968115
zbMATH Keywords: Morse-Bott functions
zbMATH Keywords: Lusternik-Schnirelmann category
zbMATH Keywords: homogeneus spaces
zbMATH Keywords: symmetric Riemannian spaces
zbMATH Keywords: cone-decomposition
zbMATH Keywords: ANR space
zbMATH Keywords: NDR pair
MaRDI profile type: Publication
full work available at URL: s11784-010-0041-9
OpenAlex ID: W2044801340
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DOI: 10.1007/S11784-010-0041-9
description: scientific article; zbMATH DE number 5968115