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 (CP 1 , 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.