Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the autonomous metric on groups of Hamiltonian diffeomorphisms of
  closed hyperbolic surfaces   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.

1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom