QUASI-morphisms and L p-metrics on groups of volume-preserving diffeomorphisms

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Abstract

Let M be a smooth compact connected oriented manifold of dimension at least two endowed with a volume form μ. We show that every homogeneous quasi-morphism on the identity component Diff 0(M, μ) of the group of volume-preserving diffeomorphisms of M, which is induced by a quasi-morphism on the fundamental group π 1(M), is Lipschitz with respect to the L p-metric on Diff 0(M, μ). As a consequence, assuming certain conditions on π 1(M), we construct bi-Lipschitz embeddings of finite dimensional vector spaces into Diff 0(M, μ).

Original languageEnglish
Pages (from-to)255-270
Number of pages16
JournalJournal of Topology and Analysis
Volume4
Issue number2
DOIs
StatePublished - 1 Jun 2012
Externally publishedYes

Keywords

  • Diffeomorphisms groups
  • bi-Lipschitz embeddings
  • braid groups
  • quasi-morphisms
  • right-invariant metrics

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