Contact invariants of \(\mathbb{Q}\)-Gorenstein toric contact manifolds, the Ehrhart polynomial and Chen-Ruan cohomology (Q6175949)

The authors consider cylindrical contact homology invariants of a \(\mathbb{Q}\)-Gorenstein toric contact manifold. Such manifolds are determined by the so-called toric diagrams. It is proved that the contact Betti numbers are toric contact invariants of \(\mathbb{Q}\)-Gorenstein toric contact manifolds. The main result shows how the contact Betti numbers of a \(\mathbb{Q}\)-Gorenstein toric contact manifold are determined by the Chen-Ruan orbifold cohomology.