Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New structures for colored HOMFLY-PT invariants   In this paper, we present several new structures for the colored HOMFLY-PT
invariants of framed links. First, we prove the strong integrality property for
the normalized colored HOMFLY-PT invariants by purely using the HOMFLY-PT skein
theory developed by H. Morton and his collaborators. By this strong integrality
property, we immediately obtain several symmetric properties for the full
colored HOMFLY-PT invariants of links. Then, we apply our results to refine the
mathematical structures appearing in the Labastida-Mari\~no-Ooguri-Vafa (LMOV)
integrality conjecture for framed links. As another application of the strong
integrality, we obtain that the $q=1$ and $a=1$ specializations of the
normalized colored HOMFLY-PT invariant are well-defined link polynomials. We
find that a conjectural formula for the colored Alexander polynomial which is
the $a=1$ specialization of the normalized colored HOMFLY-PT invariant implies
that a special case of the LMOV conjecture for frame knot holds.

18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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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: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex