Tight contact structures via dynamics
Joint work with Robert Ghrist.
Proceedings of the AMS 127 (1999), 3697-3706.

We consider the problem of realizing tight contact structures on closed orientable three-manifolds.By applying the theorems of Hofer et al., one may deduce tightness from dynamical properties of (Reeb) flows transverse to the contact structure. We detail how two classical constructions, Dehn surgery and branched covering, may be performed on certain links in such a way as to preserve a transverse tight contact structure, yielding explicit constructions of tight contact structures on several classes of three-manifolds.

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