Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadrisecant approximation of hexagonal trefoil knot   It is known that every nontrivial knot has at least two quadrisecants. Given
a knot, we mark each intersection point of each of its quadrisecants. Replacing
each subarc between two nearby marked points with a straight line segment
joining them, we obtain a polygonal closed curve which we will call the
quadrisecant approximation of the given knot. We show that for any hexagonal
trefoil knot, there are only three quadrisecants, and the resulting
quadrisecant approximation has the same knot type.

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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an