Asian Journal of Mathematics

Volume 19 (2015)

Number 3

A higher dimensional foliated Donaldson theory, I

Pages: 527 – 554

DOI: http://dx.doi.org/10.4310/AJM.2015.v19.n3.a6

Author

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

Abstract

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.

Keywords

Riemannian foliation, foliated anti-self duality, transverse anti-self duality, taut foliation, pseudogroup, foliation cycle

2010 Mathematics Subject Classification

Primary 57R57. Secondary 53C12, 58H10.

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