Seiberg–Witten invariants on manifolds with Riemannian foliations of codimension 4.

We define Seiberg–Witten equations on closed manifolds endowed with a Riemannian foliation of codimension 4. When the foliation is taut, we show compactness of the moduli space under some hypothesis satisfied for instance by closed K -contact manifolds. Furthermore, we prove some vanishing and non-vanishing results and we highlight that the invariants may be used to distinguish different foliations on diffeomorphic manifolds. [ABSTRACT FROM AUTHOR]