All Questions
Tagged with qa.quantum-algebra knot-theory
56 questions
1
vote
3
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995
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SO(3) knot polynomials
Can one use the real lie algebra so(3) to get knot polynomials? If so, do they have a skein relation (I presume they would, if they come from R-matrices in some standard way. If so, is the R-matrix ...
- 1,129
18
votes
4
answers
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Who thought that the Alexander polynomial was the only knot invariant of its kind?
I apologize that this is vague, but I'm trying to understand a little bit of the historical context in which the zoo of quantum invariants emerged.
For some reason, I have in my head the folklore:
...
- 1,756
7
votes
2
answers
497
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Computations of the Link homology categorifying the second colored Jones polynomial
Has anybody done computations of such a theory? Is there a place I could look up and see what the answers are for low crossing knots?
- 3,474
8
votes
2
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What is the Alexander polynomial of a point?
According to the Baez-Dolan cobordism hypothesis, an extended TQFT is determined by its value on a single point. This value a fully dualizable object of a symmetric monoidal $n$ category (a fully ...
- 22.1k
19
votes
4
answers
2k
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What are the points of Spec(Vassiliev Invariants)?
Background
Recall that a (oriented) knot is a smoothly embedded circle $S^1$ in $\mathbb R^3$, up to some natural equivalence relation (which is not quite trivial to write down). The collection of ...
- 54.6k
28
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2
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3k
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Why is the Alexander polynomial a quantum invariant?
When we think of quantum invariants, we usually think of the Jones polynomial or of the coloured HOMFLYPT. But (arguably) the simplest example of a quantum invariant of a knot or link is its Alexander ...
- 22.1k