Questions tagged [homflypt-polynomial]
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7 questions
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Coloured Jones polynomial of the mirror image of a multicomponent link
This question has been reposted from MathStackExchange
It is well understood that the usual Jones polynomial of a knot or link can be related to the Jones polynomial of the mirror image of the knot/...
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Computation of Colored HOMFLY Polynomials
I am trying to understand the colored HOMFLY polynomials. The theoretic description Anna Aiston gave in her PhD thesis is really nice, but what about the computation?
I would like to understand the ...
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Unusual skein relation in HOMFLY polynomial
If I take the HOMFLY(PT) polynomial defined by
$$l \,P(L_+) + l^{-1}\,P(L_-) + m\,P(L_0) = 0,$$
I have looked at expressions of the form
(knots that are the same except inside a small disk, where ...
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Proving knot polynomial dependencies and skein relations
I have two questions:
From the definition of the Jones polynomial as the normalization of the Kauffman bracket $(-A^3)^{-w(D)} \langle D\rangle$ and substituting $A\rightarrow t^{-1/4}$, how does one ...
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Categorifying skein algebras?
We can obtain the Jones polynomial by the Temperly-Lieb algebra and the HOMFLYPT polynomial from the Hecke algebra. Were there attempts to categorify the algebras itself and obtain the Khovanov ...
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HOMFLYPT vs. Jones vs. Alexander polynomial?
I'm searching for examples (perhaps the simplest one?) to show that the HOMFLYPT polynomial is stronger than the Jones and Alexander polynomial, respectively.
Any ideas what is the 1st knot in the ...
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Is the HOMFLY Polynomial the best knot invariant? [closed]
Is the HOMFLY Polynomial the best polynomial invariant that can be calculation from skein relation?
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