Geodesic
Spaces of Hermitian triples and the Seiberg--Witten equations
Izvestiya. Mathematics , Tome 65 (2001) no. 1, pp. 181-205

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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. 
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     author = {N. A. Tyurin},
     title = {Spaces of {Hermitian} triples and the {Seiberg--Witten} equations},
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N. A. Tyurin. Spaces of Hermitian triples and the Seiberg--Witten equations. Izvestiya. Mathematics , Tome 65 (2001) no. 1, pp. 181-205. http://geodesic.mathdoc.fr/item/IM2_2001_65_1_a8/