Integral Gromov-Witten invariants and complex derived orbifold bordism

Because of the presence of non-trivial automorphisms of stable maps, Gromov-Witten invariants of a general symplectic manifold are usually rational-valued. Realizing a proposal of Fukaya-Ono back in the 1990s, I will explain how to construct integer-valued Gromov-Witten type invariants by virtually counting stable maps with trivial automorphism groups after a suitable abstract perturbation of the Cauchy-Riemann equation. I will also discuss how this idea would fit into a program initiated by Abouzaid-McLean-Smith and Pardon on finding refinements of Gromov-Witten invariants with values in generalized cohomology theory.

This is based on joint work with Guangbo Xu.