On Sandon-type metrics for contactomorphism groups

Maia Fraser*, Leonid Polterovich, Daniel Rosen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish
Pages (from-to)191-214
Number of pages24
JournalAnnales Mathematiques du Quebec
Issue number2
StatePublished - 1 Oct 2018


FundersFunder number
National Science FoundationDMS-1006610
European Research Council338809
Israel Science Foundation178/13, 509/07


    • Conjugation Invariant norm
    • Contact manifold
    • Contactomorphism


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