Givental, Alexander B. Semisimple Frobenius structures at higher genus. (English) Zbl 1074.14532 Int. Math. Res. Not. 2001, No. 23, 1265-1286 (2001). 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. Cited in 5 ReviewsCited in 101 Documents MSC: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds PDFBibTeX XMLCite \textit{A. B. Givental}, Int. Math. Res. Not. 2001, No. 23, 1265--1286 (2001; Zbl 1074.14532) Full Text: DOI arXiv