Algebraic and Geometric Topology 3 (2003), paper no. 43, pages 1225-1256.

Existence of foliations on 4-manifolds

Alexandru Scorpan

Abstract. We present existence results for certain singular 2-dimensional foliations on 4-manifolds. The singularities can be chosen to be simple, for example the same as those that appear in Lefschetz pencils. There is a wealth of such creatures on most 4-manifolds, and they are rather flexible: in many cases, one can prescribe surfaces to be transverse or be leaves of these foliations.
The purpose of this paper is to offer objects, hoping for a future theory to be developed on them. For example, foliations that are taut might offer genus bounds for embedded surfaces (Kronheimer's conjecture).

Keywords. Foliation, four-manifold, almost-complex

AMS subject classification. Primary: 57R30. Secondary: 57N13, 32Q60.

DOI: 10.2140/agt.2003.3.1225

E-print: arXiv:math.GT/0302318

Submitted: 26 February 2003. (Revised: 8 December 2003.) Accepted: 12 December 2003. Published: 13 December 2003.

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Alexandru Scorpan
Department of Mathematics, University of Florida
358 Little Hall, Gainesville, FL 32611--8105, USA
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