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

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 invariant Morse theory.

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Published 1 January 2001