Shisen Luo

Ph.D. (2013) Cornell University

First Position

Associate, Goldman Sachs

Dissertation

Hard Lefschetz Property of Hamiltonian GKM Manifolds

Advisor

Tara Holm

Research Area

symplectic geometry

Abstract

The equivariant and ordinary cohomology of Hamiltonian GKM manifolds can be computed using the combinatorial data of the associated GKM graph. By studying the combinatorics of the graph, we deduce an upper bound on the second Betti number of Hamiltonian GKM manifolds. In dimension 8 and 10, this allows us to conclude that the even Betti numbers are non-decreasing up to half dimension for these manifolds.