Journal of Symplectic Geometry
Volume 1 (2001)
Existence of perfect Morse functions of spaces with semi-free circle action
Pages: 829 – 850
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.