Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Diagrammatic Construction of Third Homology Classes of Knot Quandles   We construct elements of the third quandle homology groups of knot quandles,
which are called the shadow fundamental classes. They play the same roles for
the shadow quandle cocycle invariants of knots as the fundamental classes of
knot quandles does for the quandle cocycle invariants. As an application of the
shadow fundamental classes, we show the relation between the shadow quandle
cocycle invariants and the based shadow quandle cocycle invariants. Moreover,
we will show, for a prime knot, that any third quandle homology classes are
considered as images of the shadow fundamental classes of some links.

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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: econ
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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: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat