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arXiv · 1404.6072

Unimodality of the Betti numbers for Hamiltonian circle actions with index-increasing moment maps

Yunhyung Cho
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Abstract

The unimodality conjecture posed by Tolman in the conference `Moment maps in Various Geometry" in 2005 states that if (M,w) is a 2n-dimensional smooth compact symplectic manifold equipped with a Hamiltonian circle action with only isolated fixed points, then the sequence of Betti numbers is unimodal. Recently, the author and M. Kim proved that the unimodality holds in eight-dimensional cases by using equivariant cohomology theory. In this paper, we generalize the idea in \cite{CK} to an arbitrary dimensional case. Also, we prove the conjecture in arbitrary dimension with an assumption that a moment map "index-increasing."

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Yunhyung Cho. 2015-03-09. Unimodality of the Betti numbers for Hamiltonian circle actions with index-increasing moment maps. https://arxiv.org/abs/1404.6072

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