Contact homology of good toric contact manifolds

Abstract

In this paper we show that any good toric contact manifold has 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-Martelli-Sparks-Waldram on Sasaki-Einstein metrics. We show in particular that these give rise to a new infinite family of non-equivalent contact structures on $S^2\times S^3$ in the unique homotopy class of almost contact structures with vanishing first Chern class.

30 pages. Version 2: minor corrections, improved exposition and expanded subsection 6.2 (see Remark 1.5). Version 3: minor corrections, clarified assumptions in section 4, added references, to appear in Compositio Mathematica

References in corpus (2)

• Inequivalent contact structures on Boothby-Wang 5-manifolds
• Contact homology of $S^1$-bundles over some symplectically reduced orbifolds

Cited by in corpus (11)

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• Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$
• On the Equivalence Problem for Toric Contact Structures on S^3-bundles over S^2$
• Quasi-morphisms on contactomorphism groups and contact rigidity
• Symplectic homology of some Brieskorn manifolds
• Cohomology rings of good contact toric manifolds
• Two closed orbits for non-degenerate Reeb flows
• On the Conley Conjecture for Reeb Flows
• Perfect Reeb flows and action-index relations
• On displaceability of pre-Lagrangian fibers in contact toric manifolds
• Equivariant symplectic homology of Anosov contact structures