Asymptotically holomorphic theory for symplectic orbifolds

Contact homology and higher dimensional closing lemmas

“…A key technical difficulty is our use of a flag of Reeb invariant contact sub-manifolds of ∂E in Theorem 1.12. A possible analogue of this flag can be constructed using the orbifold Donaldon divisor construction [11] on the orbifold quotient Y /R. We conclude by noting that the spectral gap provides a criterion for periodicity; a similar statement for ECH spectral invariants was proved by Cristofaro-Gardiner-Mazzuchelli [7].…”