Algebraic & Geometric Topology

Existence of foliations on 4–manifolds

Alexandru Scorpan

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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).

Article information

Source
Algebr. Geom. Topol., Volume 3, Number 2 (2003), 1225-1256.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882434

Digital Object Identifier
doi:10.2140/agt.2003.3.1225

Mathematical Reviews number (MathSciNet)
MR2026332

Zentralblatt MATH identifier
1052.57040

Subjects
Primary: 57R30: Foliations; geometric theory
Secondary: 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx] 32Q60: Almost complex manifolds

Keywords
foliation four-manifold almost-complex

Citation

Scorpan, Alexandru. Existence of foliations on 4–manifolds. Algebr. Geom. Topol. 3 (2003), no. 2, 1225--1256. doi:10.2140/agt.2003.3.1225. https://projecteuclid.org/euclid.agt/1513882434


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