On Equivariant Gromov--Witten Invariants of Resolved Conifold with Diagonal and Anti-Diagonal Actions

Abstract

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.

arXiv comment26 pages

References in corpus (12)

• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• The intrinsic normal cone
• Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation
• The Topological CP^1 Model and the Large-N Matrix Integral
• Virasoro Symmetries of the Extended Toda Hierarchy
• On the Genus Expansion in the Topological String Theory
• Functional representation of the Ablowitz-Ladik hierarchy
• The local Gromov-Witten theory of CP^1 and integrable hierarchies
• Integrable hierarchies and the mirror model of local CP1
• Generating series for GUE correlators
• Generalized Legendre transformations and symmetries of the WDVV equations
• On the Genus Two Free Energies for Semisimple Frobenius Manifolds

Cited by in corpus (1)

• Grothendieck's Dessins d'Enfants in a Web of Dualities. III