Splitting formulas for the local real Gromov-Witten invariants

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.