Tight contact structures via dynamics. (English) Zbl 0962.53048
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) flows transverse to the contact structure. We detail how two classical constructions, Dehn surgery and branched covering, may be performed on dynamically-constrained links in such a way as to preserve a transverse tight contact structure.
Reviewer: Jih-Hisin Cheng (Taipei)
MSC:
53D35 | Global theory of symplectic and contact manifolds |
57M12 | Low-dimensional topology of special (e.g., branched) coverings |
53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |