Solomon-Tukachinsky's vs. Welschinger's Open Gromov-Witten Invariants of Symplectic Sixfolds

Abstract

Our previous paper describes a geometric translation of the construction of open Gromov-Witten invariants by J. Solomon and S. Tukachinsky from a perspective of $A_{\infty}$-algebras of differential forms. We now use this geometric perspective to show that these invariants reduce to Welschinger's open Gromov-Witten invariants in dimension 6, inline with their and G. Tian's expectations. As an immediate corollary, we obtain a translation of Solomon-Tukachinsky's open WDVV equations into relations for Welschinger's invariants.