12, 24 and Beyond
Combinatorics
2016-04-04 v1 Algebraic Geometry
Symplectic Geometry
Abstract
We generalize the well-known "12" and "24" Theorems for reflexive polytopes of dimension 2 and 3 to any smooth reflexive polytope. Our methods apply to a wider category of objects, here called reflexive GKM graphs, that are associated with certain monotone symplectic manifolds which do not necessarily admit a toric action. As an application, we provide bounds on the Betti numbers for certain monotone Hamiltonian spaces which depend on the minimal Chern number of the manifold.
Cite
@article{arxiv.1604.00277,
title = {12, 24 and Beyond},
author = {Leonor Godinho and Frederik von Heymann and Silvia Sabatini},
journal= {arXiv preprint arXiv:1604.00277},
year = {2016}
}
Comments
39 pages, 4 figures