Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy, Weil-Petersson translation distance and Gromov norm for surface
  automorphisms   Thanks to a theorem of Brock on comparison of Weil-Petersson translation
distances and hyperbolic volumes of mapping tori for pseudo-Anosovs, we prove
that the entropy of a surface automorphism in general has linear bounds in
terms of Gromov norm of its mapping torus from below and in bounded geometry
case from above. We also prove that the Weil-Petersson translation distance
does the same from both sides in general. The proofs are in fact immediately
derived from the theorem of Brock together with some other strong theorems and
small observations.

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The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: chem-ph