Open ${\mathbb{CP}}^1$ descendent theory I: The stationary sector

Abstract

We define stationary descendent integrals on the moduli space of stable maps from disks to $({\mathbb{CP}}^1,{\mathbb{RP}}^1)$. We prove a localization formula for the stationary theory involving contributions from the fixed points and from all the corner-strata. We use the localization formula to prove a recursion relation and a closed formula for all genus $0$ disk cover invariants in the stationary case. For all higher genus invariants, we propose a conjectural formula.

Minor changes in v3: affiliations, grant acknowledgements, and references

References in corpus (5)

• Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions and Open Gromov-Witten Invariants for an $S^1$-Equivariant Pair
• The equivariant Gromov-Witten theory of P^1
• Moduli of Open Stable Maps to a Homogeneous Space
• Fixed-point Localization for ${\mathbb{RP}}^{2m}\subset {\mathbb{CP}}^{2m}$
• Equivariant Open Gromov-Witten Theory of $\mathbb{R}{\mathbb{P}}^{2m}\hookrightarrow \mathbb{C}{\mathbb{P}}^{2m}$