Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational moves and tangle embeddings: (2,2)-moves as a case study   We classify 3-braids up to (2,2)-move equivalence and in particular we show
how to adjust the Harikae-Nakanishi-Uchida conjecture so it holds for closed
3-braids. As important steps to classify 3-braids up to (2,2)-move equivalence
we prove the conjecture for 2-algebraic links and classify (2,2)-equivalence
classes for links up to nine crossings. We analyze the behavior of Kei
(involutive quandle) associated to a link under (2,2)-moves. We construct
Burnside Kei, Q(m,n), and ask the question, motivated by classical Burnside
question: for which values of m and n, is Q(m,n) finite?

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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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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: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys