All Questions
Tagged with braided-tensor-categories knot-theory
7
questions
22
votes
3
answers
3k
views
How many definitions are there of the Jones polynomial?
Even with the connection to quantum groups being made clearer (I believe it was not known when the Jones polynomial was first introduced), it seems to me that still we don't have the "right" ...
- 18.1k
9
votes
2
answers
593
views
Why is a braided left autonomous category also right autonomous?
In Selinger, P. A survey of graphical languages for monoidal categories (New Structures for Physics, Springer, 2011, 813, 289-233), it is stated that:
Lemma 4.17 ([23, Prop. 7.2]). A braided ...
- 345
8
votes
1
answer
298
views
Is there a notion of "knot category"?
Consider a rigid braided monoidal category, with braiding $\beta_{x,y} : x \otimes y \cong y \otimes x$, and every object has a dual such that $\epsilon_x : 1 \to a \otimes a^*, \bar\epsilon_x : a^* \...
- 779
6
votes
1
answer
1k
views
Kontsevich Integral without associators?
Recall the fact that the representations of a quantum group form a braided tensor category, and this corresponds to the fact that $U_q(\mathfrak g)$ is a quasi-triangular Hopf algebra. The braiding ...
- 18.1k
6
votes
1
answer
2k
views
Understanding Penrose diagrammatical notation
I arrived to Penrose's paper Applications of negative dimensional Tensors after reading some bits of Baez's Prehistory (link) and the first two chapters of Turaev's Quantum invariants of knots and 3-...
- 12.7k
4
votes
1
answer
377
views
Motivating quantum groups from knot invariants
Quantum groups are useful for making knot/link invariants: for example, $U_q(\mathfrak{sl}_2$) you get the Jones polynomial. This boils down to the fact that $\mathcal C = \operatorname{rep }U_q(\...
- 2,213
2
votes
0
answers
64
views
Naturality of ribbon category twists
Tortile Tensor Categories by Shum defines a twist to be a natural transformation $\theta : \operatorname{Id} \to \operatorname{Id}$ satisfying some axioms. However, wikipedia and nLab worded the ...
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