Exact orbifold fillings of contact manifolds

We study exact orbifold fillings of contact manifolds using Floer theories. Motivated by Chen–Ruan's orbifold Gromov–Witten invariants, we define symplectic cohomology of an exact orbifold filling as a group using classical techniques, that is, choosing generic almost complex structures. By studying moduli spaces of pseudo‐holomorphic/Floer curves in orbifolds, we obtain various non‐existence, restrictions and uniqueness results for orbifold singularities of exact orbifold fillings of many contact manifolds. For example, we show that exact orbifold fillings of always have exactly one singularity modeled on if . Lastly, we show that in dimension at least 3 there are pairs of contact manifolds without exact cobordisms in either direction, and that the same holds for exact orbifold cobordisms in dimension at least 5.