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).

Keywords

foliation, four-manifold, almost-complex

Mathematical Subject Classification 2000

Primary: 57R30

Secondary: 57N13, 32Q60

References

Forward citations

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

Volume 3, issue 2 (2003)

Alexandru Scorpan