A note on Reeb dynamics on the tight 3-sphere

Details A note on Reeb dynamics on the tight 3-sphere A note on Reeb dynamics on the tight 3-sphere

2007-07-07

arxiv.org/abs/0707.1068v1

Mathematics

Symplectic Geometry

20 pages, no figures

Scientific paper

We show that a nondegenerate tight contact form on the 3-sphere has exactly
two simple closed Reeb orbits if and only if the differential in linearized
contact homology vanishes. Moreover, in this case the Floquet multipliers and
Conley-Zehnder indices of the two Reeb orbits agree with those of a suitable
irrational ellipsoid in 4-space.

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