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arXiv · 1207.3151

On Sandon-type metrics for contactomorphism groups

Maia Fraser·Leonid Polterovich·Daniel Rosen
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Abstract

For certain contact manifolds admitting a 1-periodic Reeb flow we construct a conjugation-invariant norm on the universal cover of the contactomorphism group. With respect to this norm the group admits a quasi-isometric monomorphism of the real line. The construction involves the partial order on contactomorphisms and symplectic intersections. This norm descends to a conjugation-invariant norm on the contactomorphism group. As a counterpoint, we discuss conditions under which conjugation-invariant norms for contactomorphisms are necessarily bounded.

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Maia Fraser, Leonid Polterovich, Daniel Rosen. 2016-10-27. On Sandon-type metrics for contactomorphism groups. https://arxiv.org/abs/1207.3151

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