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arXiv:1305.2757 [math.GT]AbstractReferencesReviewsResources

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

Michael Brandenbursky

Published 2013-05-13, updated 2014-05-30Version 4

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.

Comments: Now it is a part of arXiv:1405.7931
Categories: math.GT, math.SG
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