Journal of Differential Geometry

Tight Contact Structures on Fibred

Ko Honda, William H. Kazez, and Gordana. Matić


As a first step towards understanding the relationship between foliations and tight contact structures on hyperbolic 3-manifolds, we classify "extremal" tight contact structures on a surface bundle M over the circle with pseudo- Anosov monodromy. More specifically, there is exactly one tight contact structure (up to isotopy) whose Euler class, when evaluated on the fiber, equals the Euler characteristic of the fiber. This rigidity theorem is a consequence of properties of the action of pseudo-Anosov maps on the complex of curves of the fiber and a remarkable flexibility property of convex surfaces in M. Indeed, this flexibility can already be seen in surface bundles over the interval, where an analogous classification theorem is also established.

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J. Differential Geom., Volume 64, Number 2 (2003), 305-358.

First available in Project Euclid: 8 December 2004

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Honda, Ko; Kazez, William H.; Matić, Gordana. Tight Contact Structures on Fibred. J. Differential Geom. 64 (2003), no. 2, 305--358. doi:10.4310/jdg/1102536453.

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