Quasi-morphisms and Lp-metrics on groups of volume-preserving diffeomorphisms Academic Article uri icon

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 π1 (M), is Lipschitz with respect to the Lp-metric on Diff 0 (M, μ). As a consequence, assuming certain conditions on π1 (M), we construct bi-Lipschitz embeddings of finite dimensional vector spaces into Diff 0 (M, μ).

publication date

  • January 1, 2012