Existence of taut foliations in Seifert fibered homology 3-spheres

speaker: Shanti Caillat-Gibert (CMI, Marseille)

abstract: We focus on the existence of taut foliations on compact 3-manifolds. David Gabai solved the problem for 3-manifolds with non-trivial homology, saying that they always admit a taut foliation. It remains the case of rational homology spheres. Here, we will study the case of Seifert rational homology spheres. The main result is that a Seifert integral homology sphere which is neither S³ nor the Poincaré homology sphere, always admits a taut foliation. Nevertheless, the result is completely different when we only suppose that the rational homology of the manifold is trivial: whatever may be the number of exceptional fibers (greater than or equal to 3), there exist infinitely many manifolds without taut foliations, and there exist infinitely many manifolds which admit one. Moreover, we will discuss the relations between the geometry and the existence of taut foliation.

timetable:
Wed 25 May, 16:45 - 17:15, Aula Dini
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