On the autonomous metric on the group of area-preserving diffeomorphisms of the 2-disc

Abstract

Let $D^2$ be the open unit disc in the Euclidean plane and let $G:=Diff(D2;area)$ be the group of smooth compactly supported area-preserving diffeomorphisms of $D^2$. We investigate the properties of G endowed with the autonomous metric. In particular, we construct a bi-Lipschitz homomorphism $Z^k\to G$ of a finitely generated free abelian group of an arbitrary rank. We also show that the space of homogeneous quasi-morphisms vanishing on all autonomous diffeomorphisms in the above group is infinite dimensional.

This a revised version, to appear in Algebraic and Geometric Topology, 20 pages, 1 figure

References in corpus (1)

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

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