Distortion elements for surface homeomorphisms

作者：Militon Emmanuel^*

来源：Geometry and Topology, 2014, 18(1): 521-614.

DOI：10.2140/gt.2014.18.521

Let S be a compact orientable surface and f be an element of the group Homeo(0)(S) of homeomorphisms of S isotopic to the identity. Denote by (f) over tilde a lift of f to the universal cover (S) over tilde of S. In this article, the following result is proved: If there exists a fundamental domain D of the covering (S) over tilde -> S such that
lim(n ->+infinity) 1/n d(n) log(d(n)) = 0,
where d(n) is the diameter of (f) over tilde (n)(D), then the homeomorphism f is a distortion element of the group Homeo(0)(S).

• 出版日期2014