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Q-Gorenstein toric contact manifolds provide an interesting class of examplesof contact manifolds with torsion first Chern class. They are completelydetermined by certain rational convex polytopes, called toric diagrams, andarise both as links of toric isolated singularities and as prequantizations ofmonotone toric symplectic orbifolds. In this paper we show how the cylindricalcontact homology invariants of a Q-Gorenstein toric contact manifold arerelated to (i) the Ehrhart (quasi-)polynomial of its toric diagram; (ii) theChen-Ruan cohomology of any crepant toric orbifold resolution of itscorresponding toric isolated singularity; (iii) the Chen-Ruan cohomology of anymonotone toric symplectic orbifold base that gives rise to it throughprequantization.

Contact invariants of Q-Gorenstein toric contact manifolds, the Ehrhart polynomial and Chen-Ruan cohomology