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Contact homology of good toric contact manifolds

Part of: Symplectic geometry, contact geometry

Published online by Cambridge University Press:  09 November 2011

Miguel Abreu  and
Leonardo Macarini
Miguel Abreu
Affiliation:
Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal (email: mabreu@math.ist.utl.pt)
Leonardo Macarini
Affiliation:
Universidade Federal do Rio de Janeiro, Instituto de Matemática, Cidade Universitária, CEP 21941-909 Rio de Janeiro, Brazil (email: leonardo@impa.br)
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Abstract

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In this paper we show that any good toric contact manifold has a well-defined cylindrical contact homology, and describe how it can be combinatorially computed from the associated moment cone. As an application, we compute the cylindrical contact homology of a particularly nice family of examples that appear in the work of Gauntlett et al. on Sasaki–Einstein metrics. We show in particular that these give rise to a new infinite family of non-equivalent contact structures on S2×S3 in the unique homotopy class of almost contact structures with vanishing first Chern class.

Keywords

toric contact manifoldstoric symplectic conescontact homology

MSC classification

Secondary: 53D42: Symplectic field theory; contact homology 53D20: Momentum maps; symplectic reduction 53D35: Global theory of symplectic and contact manifolds
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 1 , January 2012 , pp. 304 - 334
Copyright
Copyright © Foundation Compositio Mathematica 2011

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