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

Abstract

Let M be a smooth compact connected oriented manifold of dimension at least two endowed with a volume form. We show that every homogeneous quasi-morphism on the identity component $Dif{f}_0(M,vol)$ of the group of volume preserving diffeomorphisms of M, which is induced by a quasi-morphism on the fundamental group, is Lipschitz with respect to the L^p-metric on the group $Dif{f}_0(M,vol)$. As a consequence, assuming certain conditions on the fundamental group, we construct bi-Lipschitz embeddings of finite dimensional vector spaces into $Dif{f}_0(M,vol)$.

This is a published version

Cited by in corpus (5)

• Anti-trees and right-angled Artin subgroups of braid groups
• Quasi-morphisms on contactomorphism groups and contact rigidity
• On the autonomous metric on the group of area-preserving diffeomorphisms of the 2-disc
• The $L^p$-diameter of the group of area-preserving diffeomorphisms of $S^2$
• A short proof that the $L^p$-diameter of $Dif{f}_0(S,area)$ is infinite