12, 24 and Beyond

2016/04/01 by Leonor Godinho, Godinho, Leonor, Frederik von Heymann +3 · 1 citation
Mathematics · #14J45 #14M25 #52B20 #53D20 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1604.00277

openalex publication_date 2016/04/01 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

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.

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