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

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