Metric properties of the group of area preserving diffeomorphisms

Benaim, Michel; Gambaudo, Jean-Marc

doi:10.1090/S0002-9947-01-02808-2

Metric properties of the group of area preserving diffeomorphisms
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by Michel Benaim and Jean-Marc Gambaudo PDF

Trans. Amer. Math. Soc. 353 (2001), 4661-4672 Request permission

Abstract:

Area preserving diffeomorphisms of the 2-disk which are identity near the boundary form a group ${\mathcal D}_2$ which can be equipped, using the $L^2$-norm on its Lie algebra, with a right invariant metric. With this metric the diameter of ${\mathcal D}_2$ is infinite. In this paper we show that ${\mathcal D}_2$ contains quasi-isometric embeddings of any finitely generated free group and any finitely generated abelian free group.

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