Semisimple Frobenius structures at higher genus

Details Semisimple Frobenius structures at higher genus Semisimple Frobenius structures at higher genus

2000-08-09

arxiv.org/abs/math/0008067v4

Mathematics

Algebraic Geometry

Exposition is improved according to reader's suggestions. To appear in IMRN

Scientific paper

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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