Tight contact structures on hyperbolic three-manifolds

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ARIKAN M. F., Secgin M.

TOPOLOGY AND ITS APPLICATIONS, vol.231, pp.345-352, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 231
  • Publication Date: 2017
  • Doi Number: 10.1016/j.topol.2017.09.020
  • Journal Name: TOPOLOGY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.345-352
  • Middle East Technical University Affiliated: Yes

Abstract

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. (C) 2017 Elsevier B.V. All rights reserved.