Topological invariants from combinatorial data
Given a Hamiltonian T-space, one can encode some information of the space into a polytope. In good cases, the lengths of the edges of the polytope satisfy some identities, which could be translated into topological invariants. For example, given a reflexive polygon, the sum of the affine length of its edges and that of the edges in the polar polygon is always 12. A similar result holds for 3-dimensional polytopes. Later, Gohindo-Heymann-Sabatini generalized the result to arbitrary dimension with the extra assumption that the polytope is Delzant. In this talk, I’ll introduce how one can read off some topological information (for instance, self-intersection numbers, the area of invariant submanifolds, equivariant cohomology ring etc.) from the combinatorial date associated to a Hamiltonian T-space. Time permitting, I’ll sketch the proof of the result from Godinho-Heymann-Sabatini.
