Existence of Taut foliations on Seifert fibered homology 3-spheres

Details Existence of Taut foliations on Seifert fibered homology 3-spheres Existence of Taut foliations on Seifert fibered homology 3-spheres

2011-01-19

arxiv.org/abs/1101.3710v2

Mathematics

Geometric Topology

34 pages, 1 figure

Scientific paper

This paper concerns the problem of existence of taut foliations among 3-manifolds. Since the contribution of David Gabai, we know that closed 3-manifolds with non-trivial second homology group admit a taut foliations. 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 prove that all but the 3-sphere and the Poincar\'e 3-sphere admit a taut foliation. Concerning non-integral homology 3-spheres, we prove there are infinitely many which admit a taut foliation, and infinitely many without taut foliation. Moreover, we show that the geometries do not determine the existence of taut foliations on non-integral Seifert fibered homology 3-spheres.

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