Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed essential surfaces in the complements of large volume Berge knots   We construct an algorithm that lists all closed essential surfaces in the
complement of a knot that lies on the fiber of a trefoil or figure eight knot.
Such knots are Berge knots and hence admit lens space surgeries. Furthermore
they may have arbitrarily large hyperbolic volume. Using this algorithm we
concoct large volume Berge knots of two flavors: those whose complement
contains arbitrarily many distinct closed essential surfaces, and those whose
complement contains no closed essential surfaces.

18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
31
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: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: dg-ga