Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L-space knots with tunnel number >1 by experiment   In Dunfield's catalog of the hyperbolic manifolds in the SnapPy census which
are complements of L-space knots in $S^3$, we determine that $22$ have tunnel
number $2$ while the remaining all have tunnel number $1$. Notably, these $22$
manifolds contain $9$ asymmetric L-space knot complements. Furthermore, using
SnapPy and KLO we find presentations of these $22$ knots as closures of
positive braids that realize the Morton-Franks-Williams bound on braid index.
The smallest of these has genus $12$ and braid index $4$.

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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom