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

Brandenbursky, Michael¹ ; Kędra, Jarek²

¹Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA
²Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3UE, UK

Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 795-816

Résumé

Let D2 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 D2. For every natural number k we construct an injective homomorphism Zk →G, which is bi-Lipschitz with respect to the word metric on Zk and the autonomous metric on G. We also show that the space of homogeneous quasimorphisms vanishing on all autonomous diffeomorphisms in the above group is infinite-dimensional.

Détail

DOI : 10.2140/agt.2013.13.795

Classification : 57S05
Keywords: area-preserving diffeomorphisms, braid groups, quasimorphisms, quasi-isometric embeddings, bi-invariant metrics

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