Algebraic & Geometric Topology

Existence of foliations on 4–manifolds

Alexandru Scorpan

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

foliation four-manifold almost-complex


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

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