Example of an unbounded diffeomorphism group

Abstract

It is shown that the compactly supported identity component of the diffeomorphism group of the 2-dimensional punctured torus ${\mathbb{T}}_p^2$ is an unbounded group. It follows that the fragmentation norm of ${\mathbb{T}}_p^2$ is unbounded.

This paper has been withdrawn by the author since Prop. 0.3 is false