On the Mean Euler Characteristic of Gorenstein Toric Contact Manifolds

Author:

Abreu Miguel1,Macarini Leonardo12

Affiliation:

1. Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, Lisboa, Portugal

2. Universidade Federal do Rio de Janeiro, Instituto de Matemática, Cidade Universitária, Rio de Janeiro, Brazil

Abstract

Abstract We prove that the mean Euler characteristic of a Gorenstein toric contact manifold, that is, a good toric contact manifold with zero 1st Chern class, is equal to half the normalized volume of the corresponding toric diagram and give some applications. A particularly interesting one, obtained using a result of Batyrev and Dais, is the following: twice the mean Euler characteristic of a Gorenstein toric contact manifold is equal to the Euler characteristic of any crepant toric symplectic filling, that is, any toric symplectic filling with zero 1st Chern class.

Funder

FCT/Portugal

Institut Mittag-Leffler, Sweden

CNPq/Brazil

European Union

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Contact invariants of Q-Gorenstein toric contact manifolds, the Ehrhart polynomial and Chen-Ruan cohomology;Advances in Mathematics;2023-09

2. Two closed orbits for non-degenerate Reeb flows;Mathematical Proceedings of the Cambridge Philosophical Society;2020-02-21

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