On Sandon-type metrics for contactomorphism groups

Maia Fraser, Leonid Polterovich, Daniel Rosen

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)191-214
Number of pages24
JournalAnnales Mathematiques du Quebec
Volume42
Issue number2
DOIs
StatePublished - 1 Oct 2018

Keywords

  • Conjugation Invariant norm
  • Contact manifold
  • Contactomorphism

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