\'el\'ements de distorsion du groupe des diff\'eomorphismes isotopes \`a l'identit\'e d'une vari\'et\'e compacte

TL;DR

This paper studies the group of diffeomorphisms isotopic to the identity on compact manifolds, showing recurrent elements are distortions, extending known results from circle diffeomorphisms to higher dimensions.

Contribution

It generalizes Avila's theorem to compact manifolds and offers a new proof that all elements are distorted on spheres within the group of isotopic homeomorphisms.

Findings

Recurrent elements in the group are distortions.

Extension of Avila's theorem to higher-dimensional manifolds.

New proof that all elements are distorted on spheres.

Abstract

We consider, on a compact manifold, the group of diffeomorphisms that are isotopic to the identity. We show that every recurrent element is a distorsion element. This generalizes Avila's theorem on circle diffeomorphisms. The method also provides a new proof of a result by Calegari and Freedman: on a sphere, in the group of homeomorphisms that are isotopic to the identity, every element is distorted.