Metric properties of the group of area preserving diffeomorphisms

Authors
Benaim, M Gambaudo, JM
Citation
M. Benaim et Jm. Gambaudo, Metric properties of the group of area preserving diffeomorphisms, T AM MATH S, 353(11), 2001, pp. 4661-4672
Citations number
13
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
353
Issue
11
Year of publication
2001
Pages
4661 - 4672
Database
ISI
SICI code
0002-9947(2001)353:11<4661:MPOTGO>2.0.ZU;2-7
Abstract
Area preserving diffeomorphisms of the 2-disk which are identity near the b oundary form a group D-2 which can be equipped, using the L-2-norm on its L ie algebra, with a right invariant metric. With this metric the diameter of D-2 is infinite. In this paper we show that D-2 contains quasi-isometric e mbeddings of any finitely generated free group and any finitely generated a belian free group.