# Tagged Questions

**7**

votes

**1**answer

189 views

### Does the limit in the Volume conjecture converge?

The Volume conjecture says that if $J_n(q)$ are the colored Jones polynomials of a knot $K \subset S^3$, then
$$\lim_{N \to \infty} \frac{ 2 \pi}N \left\vert J_N(e^{2\pi i / N})\right\vert = vol(K)$$
...

**6**

votes

**1**answer

274 views

### Are Turaev--Viro invariants secretly a discretized path integral?

Turaev--Viro http://www.ams.org/mathscinet-getitem?mr=1191386 defined an invariant of three-manifolds $M$ denoted $TV(M)$, which was subsequently shown by Kevin Walker to coincide with ...

**7**

votes

**1**answer

292 views

### Reference request: the “Kauffman bracket skein category”?

There should be a category $3\text{CobTang}$ whose
objects are some kind of surfaces with a finite set of marked points
morphisms $M : S \to T$ are some kind of $3$-dimensional cobordisms ...

**4**

votes

**0**answers

272 views

### On finding A-polynomials

I have two questions to obtain the explicit forms of A-polynomials.
Takata used the mathematica pacage qMultisum.m to obtain the recursion relation of the colored Jones polynomials for twist knots. ...

**4**

votes

**1**answer

535 views

### Closed formula for colored Jones polynomial of the trefoil? (reference request)

(EDIT: Powers of $q$ in the formula corrected.)
I've been doing some computations with skein modules, and I found the following formula for the N-th colored Jones polynomial of the trefoil:
...

**32**

votes

**2**answers

2k views

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

The two standard approaches to the quantization of Chern-Simons theory are geometric quantization of character varieties, and quantum groups plus skein theory. These two approaches were both first ...

**2**

votes

**1**answer

344 views

### Why is the quantum Lorentz group not connected?

Podles and Woronowicz' construct the quantum Lorentz group, by which they mean $SL_q(2,\mathbb{C})$, as a quantum double of the compact quantum group $SU_q(2)$. More precisely, it is a bicrossed ...

**9**

votes

**0**answers

409 views

### Representations of quantum groups at roots of unity

I'm interested in the semisimplified category of representations of a quantum group at a root of unity. I've heard that simple objects in this category correspond to certain "integral" conjugacy ...

**6**

votes

**1**answer

307 views

### Quantum coordinate ring at root of unity

Noah Snyder gave a great answer to this question about different versions of a quantum group $U_q(\mathfrak g)$ when $q$ is a root of unity. I want to ask about forms of the deformed coordinate ring ...

**7**

votes

**2**answers

586 views

### Quantum E6/E7 knot polynomials

Has anybody seen seen quantum knot invariants associated to (E6, 27) or (E7, 56) worked out in the literature? Even for just simple knots like the trefoil or figure-8?
I suspect these haven't been ...

**4**

votes

**1**answer

215 views

### What vector space does the Kauffman bracket skein algebra of FxI act on?

The Kauffman bracket skein module $K_t(F\times I)$ (where $t$ is an indeterminant and $F$ is a closed surface) is an associative algebra (the operation being "stacking" links in the $I$ direction). ...

**3**

votes

**1**answer

511 views

### What if I change field in a Topological Quantum Field Theory?

Of course I'm talking about the algebraic notion of field.
In a few words, if a TQFT consists of a functor $Z\colon Cob(n)\to \mathbf{Vec}_k$, I'm wondering if there are sensible relations among ...

**15**

votes

**3**answers

4k views

### Quantum mathematics?

"Quantum" as a term/prefix used to be genuinely physical: what was supposed to be physically continuous turned out to be physically quantized.
What sense does this distinction make inside ...

**10**

votes

**0**answers

641 views

### Is there an “arithmetic cobordism category”?

This question is a clumsy attempt to apply a certain analogy. I hope that if the answer is negative it comes with a clarification of the scope and limitations of the analogy.
Arithmetic topology is ...

**1**

vote

**3**answers

738 views

### 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 ...

**16**

votes

**3**answers

1k views

### Is there a volume conjecture for closed 3-manifolds?

A typical statement of the volume conjecture, for instance in Murakami's survey 1002.0126, is
Conjecture: For $K$ a knot in $S^3$, the N-th colored Jones polynomials are related to the volume of ...

**18**

votes

**2**answers

1k views

### 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 ...