Morse-Bott functions and the Lusternik-Schnirelmann category
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)].
scientific article; zbMATH DE number 5968115
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