Fixed-point Localization for ${\mathbb{RP}}^{2m}\subset {\mathbb{CP}}^{2m}$

Abstract

We derive a fixed-point formula for integrals on moduli spaces of stable maps to projective spaces of even dimension. This gives a formula for the equivariant open Gromov-Witten invariants of (RP^{2m},CP^{2m}) and the structure constants of the equivariant Fukaya A-infinity algebra of RP^2m in CP^{2m} with bulk deformations. The formula involves contributions from Givental's correlators for the closed theory and the descendent integrals of discs, and specializes to give a new expression for the Welschinger count of real rational curves in the plane passing through some real and conjugation invariant pairs of points.

References in corpus (8)

• Cyclic symmetry and adic convergence in LagrangianFloer theory
• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• On manifolds with corners
• Rational curves on hypersurfaces [after A. Givental]
• Intersection theory on moduli of disks, open KdV and Virasoro
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• Counting genus zero real curves in symplectic manifolds
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Cited by in corpus (2)

• Point-like bounding chains in open Gromov-Witten theory
• Open ${\mathbb{CP}}^1$ descendent theory I: The stationary sector