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

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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.
Original languageEnglish GB
StatePublished - 2013

Publication series

NameArxiv preprint

Keywords

  • math.GT
  • math.SG

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