Partially ordered groups and geometry of contact transformations

Details Partially ordered groups and geometry of contact transformations Partially ordered groups and geometry of contact transformations

1999-10-13

arxiv.org/abs/math/9910065v1

Mathematics

Symplectic Geometry

Latex, 35 pages, preliminary version

Scientific paper

We prove, for a class of contact manifolds, that the universal cover of the
group of contact diffeomorphisms carries a natural partial order. It leads to a
new viewpoint on geometry and dynamics of contactomorphisms. It gives rise to
invariants of contactomorphisms which generalize the classical notion of the
rotation number. Our approach is based on tools of Symplectic Topology.

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