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Geometry, Symmetry and Physics Seminar

Integral Gromov-Witten invariants in genus zero

Guangbo Xu, Texas A&M

Location:  email organizers for zoom
Date & time: Monday, 07 March 2022 at 1:30PM - 2:30PM

Gromov-Witten invariants of symplectic manifolds are roughly the counts of pseudoholomorphic curves subjected to certain constraints. Because there are curves with nontrivial automorphisms, the invariants are essentially certain orbifold Euler characteristics. Hence the counts are in general rational numbers. In 1990s Fukaya and Ono proposed a method of defining an integer version of Gromov-Witten invariants using the (stable) almost complex structure on the moduli spaces. These integers can be viewed as the counts of pseudoholomorphic curves with trivial automorphism groups. Recently joint with Shaoyun Bai, we rigorously defined an integral Euler cycle of stable almost complex orbifold following Fukaya-Ono's proposal. As an application, using the recent construction of global Kuranishi charts on moduli spaces of genus zero pseudoholomorphic curves by Abouzaid-McLean-Smith, we defined the integer version of Gromov-Witten invariants in genus zero. This talk is based on the preprint

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