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Tight contact structures on hyperbolic three-manifolds

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2017-11-01
Arıkan, Mehmet Fırat
Secgin, Merve
Let Sigma(g) denote a closed orientable surface of genus g >= 2. We consider a certain infinite family of Sigma(g)-bundles over circle whose monodromies are taken from some collection of pseudo-Anosov diffeomorphisms. We show the existence of tight contact structure on every closed 3-manifold obtained via rational r-surgery along a section of any member of the family whenever r not equal 2g - 1. Combining with Thurston's hyperbolic Dehn surgery theorem, we obtain infinitely many hyperbolic closed 3-manifolds admitting tight contact structures.