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Semisimple Frobenius structures at higher genus. (English) Zbl 1074.14532
Summary: In the context of equivariant Gromov-Witten theory of tori actions with isolated fixed points, we compute genus \(g > 1\) Gromov-Witten potentials and their generalizations with gravitational descendents. Both formulas, with and without descendents, are stated in a form applicable to any semisimple Frobenius structure and therefore can be considered as definitions in the axiomatic context of Frobenius manifolds. In (nonequivariant) Gromov-Witten theory, they become conjectures expressing higher genus GW-invariants in terms of genus 0 GW-invariants of symplectic manifolds with generically semisimple quantum cup-product.

14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
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