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Semisimple Frobenius structures at higher genus

Alexander Givental
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Abstract

We describe genus g>1 potentials of semisimple Frobenius structures. Our formula can be considered as a definition in the axiomatic context of Frobenius manifolds. In Gromov-Witten theory, it becomes a conjecture expressing higher genus GW-invariants in terms of genus 0 GW-invariants of symplectic manifolds with generically semisimple quantum cup-product. The conjecture is supported by the corresponding theorem about equivariant GW-invariants of tori actions with isolated fixed points. The parallel theory of gravitational descendents is also presented.

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Alexander Givental. 2001-08-15. Semisimple Frobenius structures at higher genus. https://arxiv.org/abs/math/0008067

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