An Integral Euler Cycle in Normally Complex Orbifolds and Z-valued Gromov-Witten type invariants

Abstract: 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" and Brett Parker's generalization to "normally complex perturbations." One immediate application in symplectic topology is 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.