Contact homology of good toric contact manifolds

Abstract

Abstract 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 S 2 × S 3 in the unique homotopy class of almost contact structures with vanishing first Chern class.