# 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} }

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…

## 2 Citations

### Global Kuranishi charts and a product formula in symplectic Gromov-Witten theory

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- 2022

We construct global Kuranishi charts for the moduli spaces of stable pseudoholomorphic maps to a closed symplectic manifold in all genera. This is used to prove a product formula for symplectic…

### Fundamental groups of rationally connected symplectic manifolds

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. We show that the fundamental group of every enumeratively rationally connected closed symplectic manifold is ﬁnite. In other words, if a closed symplectic manifold has a non-zero Gromov-Witten…

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