• Corpus ID: 245836806

An integral Euler cycle in normally complex orbifolds and Z-valued Gromov-Witten type invariants

@inproceedings{Bai2022AnIE,
  title={An integral Euler cycle in normally complex orbifolds and Z-valued Gromov-Witten type invariants},
  author={Shaoyun Bai and Guangbo Xu},
  year={2022}
}

• Shaoyun Bai, Guangbo Xu
• Published 7 January 2022
• Mathematics

We define an integral Euler cycle for a vector bundle E over an effective orbifold X for which (E,X) is (stably) normally complex. The transversality is achieved by using Fukaya–Ono’s “normally polynomial perturbations” [FO97] and Brett Parker’s generalization [Par13] to “normally complex perturbations.” Two immediate applications in symplectic topology are the definition of integer-valued genus-zero Gromov–Witten type invariants for general compact symplectic manifolds using the global Kuranishi chart constructed by Abouzaid–McLean–Smith [AMS21], and an alternative proof of the cohomological splitting theorem for Hamiltonian fibrations over S2 with integer coefficients from [AMS21].