Semisimple Frobenius structures at higher genus

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.

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

References in corpus (2)

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• A descendent relation in genus 2

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