Algebraic and Geometric Topology 3 (2003),
paper no. 43, pages 1225-1256.
Existence of foliations on 4-manifolds
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).
Foliation, four-manifold, almost-complex
AMS subject classification.
Secondary: 57N13, 32Q60.
Submitted: 26 February 2003.
(Revised: 8 December 2003.)
Accepted: 12 December 2003.
Published: 13 December 2003.
Notes on file formats
Department of Mathematics, University of Florida
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