On equivariant Gromov-Witten invariants of resolved conifold with diagonal and anti-diagonal actions. (English) Zbl 1507.53085
Summary: We propose two conjectural relationships between the equivariant Gromov-Witten invariants of the resolved conifold under diagonal and anti-diagonal actions and the Gromov-Witten invariants of \(\mathbb{P}^1\) and verify their validity in genus zero approximation. We also provide evidences to support the validity of these relationships in genus one and genus two.
MSC:
| 53D45 | Gromov-Witten invariants, quantum cohomology, Frobenius manifolds |
| 14N35 | Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
Gromov-Witten invariants; resolved conifold; Frobenius manifold; complex projective line; topological recursion relation; Gromov-Witten invariants; resolved conifold; Frobenius manifold; complex projective line; topological recursion relationReferences:
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