Existence of Taut Foliations on Seifert Fibered Homology 3-spheres

Caillat-Gibert, Shanti ; Matignon, Daniel

Canadian journal of mathematics, Tome 66 (2014) no. 1, pp. 141-169

Résumé

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.

Détail

DOI : 10.4153/CJM-2013-011-4

Mots-clés : 57M25, 57M50, 57N10, 57M15, homology 3-spheres, taut foliation, Seifert-fibered 3-manifolds

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