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2003 Existence of foliations on 4–manifolds
Alexandru Scorpan
Algebr. Geom. Topol. 3(2): 1225-1256 (2003). DOI: 10.2140/agt.2003.3.1225

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).

Citation

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Alexandru Scorpan. "Existence of foliations on 4–manifolds." Algebr. Geom. Topol. 3 (2) 1225 - 1256, 2003. https://doi.org/10.2140/agt.2003.3.1225

Information

Received: 26 February 2003; Revised: 8 December 2003; Accepted: 12 December 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1052.57040
MathSciNet: MR2026332
Digital Object Identifier: 10.2140/agt.2003.3.1225

Subjects:
Primary: 57R30
Secondary: 32Q60, 57N13

Rights: Copyright © 2003 Mathematical Sciences Publishers

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Vol.3 • No. 2 • 2003
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