On the coarse classification of tight contact structures

Emmanuel Giroux; Ko Honda; Vincent Colin

On the coarse classification of tight contact structures

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arxiv math/0305186 v1 pith:E4YI2D5L submitted 2003-05-13 math.GT math.DGmath.SG

On the coarse classification of tight contact structures

Vincent Colin , Emmanuel Giroux , Ko Honda This is my paper

classification math.GT math.DGmath.SG

keywords contactstructurestightclasseseveryfinitelymanifoldmany

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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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Conformally symplectic topology from a dynamical viewpoint
math.SG 2026-07 accept novelty 4.0

Characteristic foliations of contact Hamiltonian manifolds determine convexity of hypersurfaces, with Morse-Smale implying convexity, C0-density of convex hypersurfaces, and C2-robust non-convex examples in dimensions ≥5.