Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The tropicalization of the moduli space of curves II: Topology and
  applications   We study the topology of the tropical moduli space parametrizing stable
tropical curves of genus g with n marked points in which the bounded edges have
total length 1, and prove that it is highly connected. Using the identification
of this space with the dual complex of the boundary in the moduli space of
stable algebraic curves, we give a simple expression for the top weight
cohomology of M_{1,n} as a representation of the symmetric group and describe
an explicit dual basis in homology consisting of abelian cycles for the pure
mapping class group.

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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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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: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an