Asian Journal of Mathematics

Volume 19 (2015)

Number 3

A higher dimensional foliated Donaldson theory, I

Pages: 527 – 554



Shuguang Wang (Department of Mathematics, University of Missouri, Columbia, Missouri, U.S.A.)


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.

Published 19 June 2015