Tight Contact Structures on Fibered Hyperbolic 3-manifolds

  title={Tight Contact Structures on Fibered Hyperbolic 3-manifolds},
  author={WILLIAM H. KAZEZ and Gordana M Mati{\'c}},
We take a first step towards understanding the relationship between foliations and universally tight contact structures on hyperbolic 3-manifolds. If a surface bundle over a circle has pseudo-Anosov holonomy, we obtain a classification of " extremal " tight contact structures. Specifically, there is exactly one contact structure whose Euler class, when evaluated on the fiber, equals the Euler number of the fiber. This rigidity theorem is a consequence of properties of the action of pseudo… CONTINUE READING


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