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Partially ordered groups and geometry of contact transformations

Yakov Eliashberg·Leonid Polterovich
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Abstract

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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Yakov Eliashberg, Leonid Polterovich. 1999-10-13. Partially ordered groups and geometry of contact transformations. https://arxiv.org/abs/math/9910065

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