Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Triple-crossing number and moves on triple-crossing link diagrams   Every link in the 3-sphere has a projection to the plane where the only
singularities are pairwise transverse triple points. The associated diagram,
with height information at each triple point, is a triple-crossing diagram of
the link. We give a set of diagrammatic moves on triple-crossing diagrams
analogous to the Reidemeister moves on ordinary diagrams. The existence of
n-crossing diagrams for every n>1 allows the definition of the n-crossing
number. We prove that for any nontrivial, nonsplit link, other than the Hopf
link, its triple-crossing number is strictly greater than its
quintuple-crossing number.

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The categories of this paper are: patt-sol
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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: dg-ga
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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: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con