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VOL. 52 | 2008 Foliations and compact leaves on 4-manifolds I. Realization and self-intersection of compact leaves
Yoshihiko Mitsumatsu, Elmar Vogt

Editor(s) Robert Penner, Dieter Kotschick, Takashi Tsuboi, Nariya Kawazumi, Teruaki Kitano, Yoshihiko Mitsumatsu


We introduce an easily tractable cohomological criterion for the existence of 2-dimensional foliations with a prescribed compact leaf on a 4-manifold relying on standard methods, Milnor's inequality for the existence of a flat connection on an $\mathbb{R}^2$-bundle over a surface, and Thurston's $h$-principle. This is used to investigate the self-intersection numbers of compact leaves of foliations on the product of two surfaces, in particular the question whether these numbers are bounded on a given 4-manifold.


Published: 1 January 2008
First available in Project Euclid: 28 November 2018

zbMATH: 1179.57042
MathSciNet: MR2509719

Digital Object Identifier: 10.2969/aspm/05210415

Rights: Copyright © 2008 Mathematical Society of Japan


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