Asian Journal of Mathematics
Volume 19 (2015)
A higher dimensional foliated Donaldson theory, I
Pages: 527 – 554
We introduce a foliated anti-self dual equation for higher dimensional smooth manifolds with codimension-$4$ Riemannian foliations. Several fundamental results including a compactification theorem for the moduli space are formulated and proved, towards the defining of a possible Donaldson type invariant for such foliated manifolds.
Riemannian foliation, foliated anti-self duality, transverse anti-self duality, taut foliation, pseudogroup, foliation cycle
2010 Mathematics Subject Classification
Primary 57R57. Secondary 53C12, 58H10.