Unimodality of Betti numbers for Hamiltonian circle actions with index-increasing moment maps (Q2810652)

The author of the paper under review proves conditions under which a \(2n\)-dimensional smooth compact symplectic manifold \((M,\omega)\) equipped with a Hamiltonian circle action with isolated fixed points has unimodal even Betti numbers. He shows that when the moment map is an index increasing function the above statement is true. He uses equivariant cohomology arguments and the Atiyah-Bott-Berline-Vergne localization theorem. He ends the paper by giving some examples.