Seiberg-Witten and Gromov invariants for self-dual harmonic 2-forms

Our earlier work (Geom. Topol. 24 (2020) 1791-1839) gives an extension of Taubes' "SW D Gr" theorem to nonsymplectic 4-manifolds. The main result of this sequel asserts the following: whenever the Seiberg-Witten invariants are defined over a closed minimal 4-manifold X, they are equivalent modulo 2 to "near-symplectic" Gromov invariants in the presence of certain self-dual harmonic 2-forms on X. A version for nonminimal 4-manifolds is also proved. A corollary to Morse theory on 3-manifolds is also announced, recovering a result of Hutchings, Lee, and Turaev about the 3-dimensional Seiberg-Witten invariants.