We define an integer-valued virtual count of embedded pseudoholomorphic curves of two times a primitive homology class and arbitrary genus in symplectic Calabi–Yau 3-folds, which can be viewed as an extension of Taubes’s Gromov invariant. The construction depends on a detailed study of bifurcations of moduli spaces of embedded pseudoholomorphic curves which is partially motivated by Wendl’s recent solution of Bryan and Pandharipande’s superrigidity conjecture.

We construct viscosity solutions to the special Lagrangian equation that are Lipschitz but not $C^1$, and have nonminimal gradient graphs.