Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Singly Periodic Genus-One Helicoid   We prove the existence of a complete, embedded, singly periodic minimal
surface, whose quotient by vertical translations has genus one and two ends.
The existence of this surface was announced in our paper in {\it Bulletin of
the AMS}, 29(1):77--84, 1993. Its ends in the quotient are asymptotic to one
full turn of the helicoid, and, like the helicoid, it contains a vertical line.
Modulo vertical translations, it has two parallel horizontal lines crossing the
vertical axis. The nontrivial symmetries of the surface, modulo vertical
translations, consist of: $180^\circ$ rotation about the vertical line;
$180^\circ$ rotation about the horizontal lines (the same symmetry); and their
composition.

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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio