Volume 18, issue 1 (2014)

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Distortion elements for surface homeomorphisms

Emmanuel Militon

Geometry & Topology 18 (2014) 521–614
Abstract

Let S be a compact orientable surface and f be an element of the group Homeo0(S) of homeomorphisms of S isotopic to the identity. Denote by f̃ a lift of f to the universal cover S̃ of S. In this article, the following result is proved: If there exists a fundamental domain D of the covering S̃ S such that

limn+1 ndn log(dn) = 0,

where dn is the diameter of f̃n(D), then the homeomorphism f is a distortion element of the group Homeo0(S).

Keywords
homeomorphism, surface, group, distortion
Mathematical Subject Classification 2010
Primary: 37C85
References
Publication
Received: 2 November 2012
Revised: 27 June 2013
Accepted: 28 July 2013
Published: 29 January 2014
Proposed: Leonid Polterovich
Seconded: Danny Calegari, Jean-Pierre Otal
Authors
Emmanuel Militon
Centre de Mathématiques Laurent Schwartz
École Polytechnique
91128 Palaiseau Cedex
France
http://www.math.u-psud.fr/~militon