# Tag Info

### Why hasn't anyone proved that the two standard approaches to quantizing Chern-Simons theory are equivalent?

The answer of Jørgen Ellegaard Andersen only concerns the case of when the gauge group is $SU(n)$. I will argue that all the ingredients for the equivalence between the two approaches (namely "...
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• 8,044
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### Examples of n+1D TQFT with 1 dimensional Hilbert spaces on n-torus and n-sphere but higher dimensional Hilbert spaces on other n-manifolds

If your topological field theory is at least once-extended, by which I mean it assigns values to $(n+1)$-manifolds, $n$-manifolds, and also to $(n-1)$-manifolds, than this cannot happen. More ...
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### Polynomial invariants for unoriented links

Colored Kauffman polynomials are independent of orientations of links. If you look at the skein relation of Kauffman polynomial, there is no arrow. This is true for colored cases. Kauffman polynomials ...
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### The Jones polynomial at specific values of $t$

The volume conjecture predicts the existence limit of (a certain normalization of) the colored Jones polynomials evaluated at roots of unity (which is not known to exist), and that this limit is equal ...
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### Non-extendable 3D TQFTs

Check out Andras Juhasz' paper: https://arxiv.org/pdf/1408.0668.pdf Specifically, Theorem 1.10: There is an equivalence between the symmetric monoidal category of (2+1)-dimensional TQFTs and the ...
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### Algebraic proof of 4-colour theorem?

There are several reformulations by Matiyasevich, like this with polynomial, this with binomial coefficients modulo 7, also some others but they are less `algebraic', whatever it means.
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### Is there a volume conjecture for closed 3-manifolds?

There's another volume conjecture formulated by Chen and Yang for Turaev-Viro invariants of closed manifolds. They present some evidence for the conjecture in the paper. In a second paper, Yang and ...
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### Polynomial invariants for unoriented links

Let $\mathfrak g$ be a simple Lie algebra, $U_q(\mathfrak g)$ the corresponding quantum group and $V$ a simple module over it. From this you get an invariant of framed oriented links. Now since $V$ is ...
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### Jones polynomial of tangles using Temperley-Lieb algbra?

Yes, the same thing can be done using in terms of the TL algebra. Namely, that is how the Jones polynomial was originally defined. For TL, there are two ways to get the link invariant, which both ...
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### Does the limit in the Volume conjecture converge?

No, this is unknown. There are heuristic arguments for convergence based on the stationary phase approximation, but as far as I know, no one has made the argument precise in general. The closest I ...
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### Why hasn't anyone proved that the two standard approaches to quantizing Chern-Simons theory are equivalent?

For future reference. The elegant argument sketched by Kevin Walker above involving pants decompositions and Bohr-Sommerfeld fibers was published by Andersen on the arXiv later that year, as part of ...
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### Relations between quantum groups at roots of unity, modular representation theory, and physics

Modular representations (representations in spaces over a field of nonzero characteristics) have been used in physics by Felix Lev to construct a quantum theory that is based on a finite number field (...
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