On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces Academic Article uri icon

abstract

  • 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.

publication date

  • January 1, 2013