Tight contact structures via dynamics

Abstract

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 ows transverse to the contact structure. We detail how t w o classical constructions, Dehn surgery and branched covering, may be performed on dynamically-constrained links in such a w a y as to preserve a transverse tight contact structure.