Guangbo Xu:Integer-valued Gromov-Witten type invariants for symplectic manifolds

Abstract:  Gromov-Witten invariants for a general target are rational-valued but not necessarily integer-valued. This is due to the contribution of curves with nontrivial automorphism groups. In 1997 Fukaya and Ono proposed a new method in symplectic geometry which can count curves with a trivial automorphism group. While ordinary Gromov-Witten invariants only use the orientation on the moduli spaces, this integer-valued counts are supposed to use also the (stable) complex structure on the moduli spaces. In this talk I will present the recent joint work with Shaoyun Bai in which we rigorously defined the integer-valued Gromov-Witten type invariants in genus zero for a symplectic manifold and describe a conjecture relating the ordinary Gromov-Witten invariants with the integer counts. This talk is based on the preprint