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On the coarse classification of tight contact structures

Vincent Colin·Emmanuel Giroux·Ko Honda
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Abstract

We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures.

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Vincent Colin, Emmanuel Giroux, Ko Honda. 2003-05-13. On the coarse classification of tight contact structures. https://arxiv.org/abs/math/0305186

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