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arXiv · 1207.0624

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

Michael Brandenbursky·Jarek Kedra
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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 $Z^k \rightarrow G$ 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.

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Michael Brandenbursky, Jarek Kedra. 2013-02-27. On the autonomous metric on the group of area-preserving diffeomorphisms of the 2-disc. https://doi.org/10.2140/agt.2013.13.795

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