Alexandru Scorpan
Published 2003-02-25, updated 2003-12-14Version 5
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).
Comments: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-43.abs.html
Journal: Algebr. Geom. Topol. 3 (2003) 1225-1256
On the connectedness of the space of codimension one foliations on a closed 3-manifold
A quick survey of foliations on 4-manifolds
Existence results of Spin$(2,n-1)_0$-pseudo-Riemannian cobordisms
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