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

Michael Brandenbursky; Jarek Kedra

doi:10.2140/agt.2013.13.795

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

Research output: Contribution to journal › Article › peer-review

Abstract

Let D² be the open unit disc in the Euclidean plane and let G:=WD 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 Z ^k → G, which is bi-Lipschitz with respect to the word metric on Z^k 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.

Original language	American English
Pages (from-to)	795-816
Number of pages	22
Journal	Algebraic and Geometric Topology
Volume	13
Issue number	2
DOIs	https://doi.org/10.2140/agt.2013.13.795
State	Published - 11 Apr 2013
Externally published	Yes

Keywords

Area-preserving diffeomorphisms
Bi-invariant metrics
Braid groups
Quasi-isometric embeddings
Quasimorphisms

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.2140/agt.2013.13.795

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AB - Let D2 be the open unit disc in the Euclidean plane and let G:=WD 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 Z k → 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.

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KW - Bi-invariant metrics

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KW - Quasi-isometric embeddings

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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