Spaces of Hermitian triples and the Seiberg–Witten equations

In [12] we described a canonical map $\tau$ of the space of all Hermitian triples to the real cohomology space. In this paper we use this map to introduce new equations, which are gauge-invariant with respect to the action of $\operatorname{Diff}^+X$. We also describe a connection between these equations and the Seiberg–Witten equations and invariants for 4-manifolds.