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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Existence of foliations on 4–manifolds

Alexandru Scorpan

Algebraic & Geometric Topology 3 (2003) 1225–1256

arXiv: math.GT/0302318

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
Mathematical Subject Classification 2000
Primary: 57R30
Secondary: 57N13, 32Q60
References
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Publication
Received: 26 February 2003
Revised: 8 December 2003
Accepted: 12 December 2003
Published: 13 December 2003
Authors
Alexandru Scorpan
Department of Mathematics
University of Florida
358 Little Hall
Gainesville, FL 32611–8105 USA
www.math.ufl.edu/~ascorpan