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Existence of Taut Foliations on Seifert Fibered Homology 3-spheres

Published online by Cambridge University Press:  20 November 2018

Shanti Caillat-Gibert  and
Daniel Matignon
Shanti Caillat-Gibert
Affiliation:
Centre de Mathématiques et Informatique, Aix-Marseille Université, 13453 Marseille Cedex 13, France e-mail: [email protected] [email protected]
Daniel Matignon
Affiliation:
Centre de Mathématiques et Informatique, Aix-Marseille Université, 13453 Marseille Cedex 13, France e-mail: [email protected] [email protected]
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Abstract

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This paper concerns the problem of existence of taut foliations among 3-manifolds. From the work of David Gabai we know that a closed 3-manifold with non-trivial second homology group admits a taut foliation. The essential part of this paper focuses on Seifert fibered homology 3-spheres. The result is quite different if they are integral or rational but non-integral homology 3-spheres. Concerning integral homology 3-spheres, we can see that all but the 3-sphere and the Poincaré 3-sphere admit a taut foliation. Concerning non-integral homology 3-spheres, we prove there are infinitely many that admit a taut foliation, and infinitely many without a taut foliation. Moreover, we show that the geometries do not determine the existence of taut foliations on non-integral Seifert fibered homology 3-spheres.

Keywords

57M2557M5057N1057M15homology 3-spherestaut foliationSeifert-fibered 3-manifolds
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 66 , Issue 1 , February 2014 , pp. 141 - 169
Copyright
Copyright © Canadian Mathematical Society 2014

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