Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automorphisms of Torelli groups   In this paper, we prove that each automorphism of the Torelli group of a
surface is induced by a diffeomorphism of the surface, provided that the
surface is a closed, connected, orientable surface of genus at least 3. This
result was previously announced by Benson Farb for genus at least 4 and has
recently been announced by Benson Farb and Nikolai Ivanov for subgroups of
finite index in the Torelli group for surfaces of genus at least 5. This result
is also directly analogous to previous results established for classical braid
groups, mapping class groups, and surface braid groups.

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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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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: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: gr-qc