Authors: Hiroyuki Kadzisa, Mamoru Mimura
Title: Morse-Bott functions and the Lusternik-Schnirelmann category, I
Email:
kadzisa@math.titech.ac.jp,
mimura@math.okayama-u.ac.jp
The Lusternik-Schnirelmann category of a space is a homotopy invariant.
Cone-decompositions are used to give an upper bound for
Lusternik-Schnirelmann categories of topological spaces.
The purpose of this paper
is to show how to construct cone-decompositions of manifolds
by using functions of class C^1 and their gradient flows,
and to apply the result to some homogeneous spaces
to determine their Lusternik-Schnirelmann categories.
In particular,
the Morse-Bott functions on the Stiefel manifolds considered by Frankel
are effectively used
for constructing all the cone-decompositions in this paper.