Distortion elements for surface homeomorphisms

Militon, Emmanuel¹

¹ Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau Cedex, France

Geometry & topology, Tome 18 (2014) no. 1, pp. 521-614.

Résumé

Let $S$ be a compact orientable surface and $f$ be an element of the group ${Homeo}_0\left(S\right)$ of homeomorphisms of $S$ isotopic to the identity. Denote by $\tilde{f}$ a lift of $f$ to the universal cover $\tilde{S}$ of $S$. In this article, the following result is proved: If there exists a fundamental domain $D$ of the covering $\tilde{S}\to S$ such that

where $d_n$ is the diameter of ${\tilde{f}}^n\left(D\right)$, then the homeomorphism $f$ is a distortion element of the group ${Homeo}_0\left(S\right)$.

Détail

DOI : 10.2140/gt.2014.18.521

Classification : 37C85
Keywords: homeomorphism, surface, group, distortion

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