Front: [arXiv:1005.3787] Contact homology of good toric contact manifolds

Title: Contact homology of good toric contact manifolds
Authors: Miguel Abreu, Leonardo Macarini
Categories: math.SG Symplectic Geometry (math.GT Geometric Topology)
Comments: 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
MSC: 53D42 (primary), 53D20, 53D35 (secondary)
Journal reference: Compositio Math. 148 (2012) 304-334 (DOI 10.1112/S0010437X11007044)

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.

Owner: Miguel Abreu
Version 1: Thu, 20 May 2010 18:44:43 GMT
Version 2: Tue, 20 Jul 2010 13:35:45 GMT
Version 3: Thu, 7 Jul 2011 09:29:39 GMT