WDVV-type relations for disk Gromov–Witten invariants in dimension 6

The first author’s previous work established Solomon’s WDVV-type relations for Welschinger’s invariant curve counts in real symplectic fourfolds by lifting geometric over possibly unorientable morphisms. We apply her framework to obtain WDVV-style the disk invariants of sixfolds with some symmetry, particular confirming Alcolado’s prediction $${\mathbb {P}}^3$$ and extending it other spaces. These reduce computation many small degrees provide lower bounds rational curves positive-dimensional insertions cases. In case , our fit perfectly Kollár’s vanishing results.