# Hamiltonian S1-spaces with large equivariant pseudo-index.

Speaker: Isabelle Charton, Universität zu Köln.

Date: 18 oct 2019, 11h. Cancelado! :(

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: Let (M,\omega) be a compact symplectic manifold of dimension 2n endowed with a Hamiltonian circle action with only isolated fixed points. Whenever M admits a toric 1-skeleton S, which is a special collection of embedded 2-spheres in M, we define the notion of equivariant pseudo-index of S: this is the minimum of the evaluation of the first Chern class c1 on the spheres of S. This can be seen as the analog in this category of the notion of pseudo-index for complex Fano varieties. In this talk we discuss upper bounds for the equivariant pseudo-index. In particular, when the even Betti numbers of M are unimodal, we prove that it is at most n+1 . Moreover, when it is exactly n+1, M must be homotopically equivalent to CPn.