English

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.

Keywords

Cite

@article{arxiv.1105.4443,
  title  = {Commutator length of annulus diffeomorphisms},
  author = {Emmanuel Militon},
  journal= {arXiv preprint arXiv:1105.4443},
  year   = {2019}
}
R2 v1 2026-06-21T18:10:59.808Z