Mathematical Research Letters

Volume 21 (2014)

Number 4

Unimodality of the Betti numbers for Hamiltonian circle action with isolated fixed points

Pages: 691 – 696



Yunhyung Cho (School of Mathematics, Korea Institute for Advanced Study, Seoul, Korea)

Min Kyu Kim (Department of Mathematics Education, Gyeongin National University of Education, Incheon, Korea)


Let $(M, \omega)$ be an eight-dimensional closed symplectic manifold equipped with a Hamiltonian circle action with only isolated fixed points. In this article, we will show that the Betti numbers of $M$ are unimodal, i.e., $b_0 (M) \leq b_2 (M) \leq b_4 (M)$.

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