Commutator length of annulus diffeomorphisms

Details Commutator length of annulus diffeomorphisms Commutator length of annulus diffeomorphisms

2011-05-23

arxiv.org/abs/1105.4443v3

Mathematics

Dynamical Systems

Scientific paper

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.

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