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A characterization of the tight 3-sphere II

โœ Scribed by H. Hofer; K. Wysocki; K. Zehnder

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
258 KB
Volume
52
Category
Article
ISSN
0010-3640

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โœฆ Synopsis

Recall that every closed, oriented, connected 3-manifold M admits a contact form ฮป. We shall give conditions on a periodic orbit P 0 of the Reeb vector field defined by ฮป that allows the construction of an open book decomposition of M \ P 0 into embedded planes asymptotic to P 0 such that P 0 is the binding orbit of the decomposition. It follows that M is the tight 3-sphere. As a by-product, a new dynamical criterion for the tightness of a contact structure is derived in the proof. The results extend earlier results.

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