Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric estimates from spanning surfaces   We derive bounds on the length of the meridian and the cusp volume of
hyperbolic knots in terms of the topology of essential surfaces spanned by the
knot. We provide an algorithmically checkable criterion that guarantees that
the meridian length of a hyperbolic knot is below a given bound. As
applications we find knot diagrammatic upper bounds on the meridian length and
the cusp volume of hyperbolic adequate knots and we obtain new large families
of knots with meridian lengths bounded above by four. We also discuss
applications of our results to Dehn surgery.

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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg