Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diameter of the thick part of moduli space and simultaneous Whitehead
  moves   Let S be a surface of genus g with p punctures with negative Euler
characteristic. We study the diameter of the $\epsilon$-thick part of moduli
space of S equipped with the Teichm\"uller or Thurston's Lipschitz metric. We
show that the asymptotic behaviors in both metrics are of order $\log
\frac{g+p}{\epsilon}$. The same result also holds for the $\epsilon$-thick part
of the moduli space of metric graphs of rank n equipped with the Lipschitz
metric. The proof involves a sorting algorithm that sorts an arbitrary labeled
tree with n labels with simultaneous Whitehead moves, where the number of steps
is of order log(n).

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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas