Commutator length of annulus diffeomorphisms
Dynamical Systems
2019-02-20 v3
Abstract
We study the group of C^{r}-diffeomorphisms of the closed annulus that are isotopic to the identity. We show that, for r different from 3, the linear space of homogeneous quasi-morphisms on this group is one dimensional. Therefore, the commutator length on this group is (stably) unbounded. In particular, this provides an example of a manifold whose diffeomorphisms group is unbounded in the sense of Burago, Ivanov and Polterovich.
Cite
@article{arxiv.1105.4443,
title = {Commutator length of annulus diffeomorphisms},
author = {Emmanuel Militon},
journal= {arXiv preprint arXiv:1105.4443},
year = {2019}
}