On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces

Abstract

Let ${\Sigma }_g$ be a closed hyperbolic surface of genus $g$ and let $Ham({\Sigma }_g)$ be the group of Hamiltonian diffeomorphisms of ${\Sigma }_g$. The most natural word metric on this group is the autonomous metric. It has many interesting properties, most important of which is the bi-invariance of this metric. In this work we show that $Ham({\Sigma }_g)$ is unbounded with respect to this metric.

arXiv commentNow it is a part of arXiv:1405.7931