Existence of foliations on 4-manifolds

Details Existence of foliations on 4-manifolds Existence of foliations on 4-manifolds

2003-02-25

arxiv.org/abs/math/0302318v5

Algebr. Geom. Topol. 3 (2003) 1225-1256

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-43.abs.html

Scientific paper

We present existence results for certain singular 2-dimensional foliations on 4-manifolds. The singularities can be chosen to be simple, e.g. the same as those that appear in Lefschetz pencils. There seems to be a wealth of such creatures on most 4-manifolds. In certain 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).

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