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Results tagged with qa.quantum-algebra
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user 5010
Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
8
votes
What are the points of Spec(Vassiliev Invariants)?
The points of Spec $V$ live n a somewhat complicated completion of the space of knots (not formal linear combinations), but I think it's illuminating to think about the case of braids and their "Vassi …
- 10.1k
27
votes
Accepted
Usefulness of using TQFTs
All the answers so far have focused on 3 dimensions, but the answer is much more striking in 4 dimensions. Freedman's theorem tells you that classical homology invariants give you complete informatio …
- 10.1k
13
votes
2
answers
1k
views
Intrinsic characterization of Soergel bimodules?
A Soergel bimodule (for $S_n$) is a bimodule over $R = \mathbb{Q}[x_1,\dots,x_n]$ which appears as a summand/grading shift of tensor products of the basic bimodules
$$B_{i,i+1} = R \otimes_{i,i+1} R$$ …
- 10.1k
16
votes
Why is a 2d TQFT formulated as a functor?
There are interesting examples where the duality you're trying to bake in does not hold. In particular, the 3+1 dimensional (pseudo-)TQFTs coming from Seiberg-Witten theory in 4 dimensions do not hav …
- 10.1k
25
votes
Accepted
Who thought that the Alexander polynomial was the only knot invariant of its kind?
The skein relation approach to knot invariants was not very popular before the Jones polynomial. The Alexander polynomial was thought of as coming from homology (of the cyclic branched cover); Conway …
- 10.1k
7
votes
What is the state in the WRT TQFT associated to a handlebody?
(Making this an answer, since it will be a little long, even though it doesn't actually answer the question.)
One thing to be aware of is that there are multiple ways to talk about this same TQFT. In …
- 10.1k