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

Abstract

Let (M,ω) 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. b0(M) ≤ b2(M) ≤ b4(M).

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