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Commutator length of annulus diffeomorphisms

Published online by Cambridge University Press:  11 December 2012

E. MILITON
E. MILITON*
Affiliation:
Laboratoire de Mathématiques d’Orsay, UMR 8628, Bât. 425, Faculté des Sciences d’Orsay, Université Paris-Sud XI, F-91405 Orsay cedex, France (email: emmanuel.militon@math.u-psud.fr)
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Abstract

We study the group Diffr0(𝔸) of Cr-diffeomorphisms of the closed annulus that are isotopic to the identity. We show that, for r≠2,3, the linear space of homogeneous quasi-morphisms on the group Diffr0(𝔸) is one-dimensional. Therefore, the commutator length on this group is (stably) unbounded. In particular, this provides an example of a manifold whose diffeomorphism group is unbounded in the sense of Burago, Ivanov and Polterovich.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 3 , June 2014 , pp. 919 - 937
Copyright
©2012 Cambridge University Press 

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