Existence of perfect Morse functions on spaces with semi-free circle action

Mikhail Kogan

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Existence of perfect Morse functions on spaces with semi-free circle action

Mikhail Kogan

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Abstract

Let $M$ be a compact oriented simply-connected manifold of dimension at least 8. Assume $M$ is equipped with a torsion-free semi-free circle action with isolated fixed points. We prove $M$ has a perfect invariant Morse-Smale function. The major ingredient in the proof is a new cancellation theorem for the invariant Morse theory.

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Mikhail Kogan. 2003-04-01. Existence of perfect Morse functions on spaces with semi-free circle action. https://arxiv.org/abs/math/0202149

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