Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: HOMFLY-PT homology for general link diagrams and braidlike isotopy   Khovanov and Rozansky's categorification of the HOMFLY-PT polynomial is
invariant under braidlike isotopies for any link diagram and Markov moves for
braid closures. To define HOMFLY-PT homology, they required a link to be
presented as a braid closure, because they did not prove invariance under the
other oriented Reidemeister moves. In this text we prove that the Reidemeister
IIb move fails in HOMFLY-PT homology by using virtual crossing filtrations of
the author and Rozansky. The decategorification of HOMFLY-PT homology for
general link diagrams gives a deformed version of the HOMFLY-PT polynomial,
$P^{b}(D)$, which can be used to detect nonbraidlike isotopies. Finally, we
will use $P^{b}(D)$ to prove that HOMFLY-PT homology is not an invariant of
virtual links, even when virtual links are presented as virtual braid closures.

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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph