Abstract.
We prove that, for a class of contact manifolds, 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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Submitted: March 2000.
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Eliashberg, Y., Polterovich, L. Partially ordered groups and geometry of contact transformations . GAFA, Geom. funct. anal. 10, 1448–1476 (2000). https://doi.org/10.1007/PL00001656
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DOI: https://doi.org/10.1007/PL00001656