Journal of Symplectic Geometry

Volume 20 (2022)

Number 3

Splitting formulas for the local real Gromov–Witten invariants

Pages: 561 – 664

DOI: https://dx.doi.org/10.4310/JSG.2022.v20.n3.a2

Authors

Penka Georgieva (Sorbonne Université, Université de Paris, CNRS, Institut de Mathématiques de Jussieu, Paris, France)

Eleny-Nicoleta Ionel (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)

Abstract

Motivated by the real version of the Gopakumar–Vafa conjecture for $3$-folds, the authors introduced in [GI] the notion of local real Gromov–Witten invariants associated to local $3$-folds over Real curves. This article is devoted to the proof of a splitting formula for these invariants under target degenerations. It is used in [GI] to show that the invariants give rise to a $2$-dimensional Klein TQFT and to prove the local version of the real Gopakumar–Vafa conjecture.

Received 13 May 2020

Received revised 7 October 2021

Accepted 19 October 2021

Published 28 February 2023