Equivariant Open Gromov-Witten Theory of ℝℙ^2m \hookrightarrow ℂℙ^2m

2017/09/26 by Amitai Netser Zernik, Zernik, Amitai Netser
Mathematics · #14N35 (Primary) 53D37 #32Q65 (Secondary) #53D12 #53D45 #55N25 #55N91 #58A10 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Finite Group Theory Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1709.09483

openalex publication_date 2017/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define equivariant open Gromov-Witten invariants for ℝℙ^2m \hookrightarrow ℂℙ^2m as sums of integrals of equivariant forms over resolution spaces, which are blowups of products of moduli spaces of stable disc-maps modeled on trees. These invariants encode the quantum deformation of the equivariant cohomology of ℝℙ^2m by holomorphic discs in ℂℙ^2m and, for m=1, specialize to give Welschinger's signed count of real rational planar curves in the non-equivariant limit.

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