All Questions
6 questions
3
votes
1
answer
374
views
On expressions of colored Jones polynomials
In the paper by Masbaum, it was shown that the colored Jones polynomials for a twist knot $K_p$ can be written as
\begin{eqnarray}
J_{n}(K_p;q)&=&\sum_{k=0}^{\infty} {\cal C}_{K_p}(k)
\...
- 4,713
10
votes
2
answers
664
views
$6j$-symbols for $U_q({\mathfrak{sl}}_n)$ and colored HOMFLY polynomials
Explicit expression of quantum $6j$-symbolos for $U_q({\mathfrak{sl}_2})$ have been known due to the work of Kirillov and Reshitikhin.
My Question:
How much are known about quantum $6j$-symbolos ...
- 630
12
votes
2
answers
789
views
Knot Invariants from Twisted Quantum Doubles
In "Topological Gauge Theories and Group Cohomology", Dijkgraaf and Witten construct a 3-manifold invariant from a finite group $G$ and 3-cocycle $\omega$. I would think there is also an associated ...
- 2,533
10
votes
1
answer
410
views
Links which HOMFLY homology distinguish but the HOMFLY polynomial does not.
Does anyone know of a pair of different links which the HOMFLY polynomial does not distinguish, but HOMFLY homology does? Or does there exist such a pair of links?
I'm assuming there does exist such ...
- 2,273
8
votes
2
answers
1k
views
AJ conjecture for links
Garoufalidis proposed a conjecture on $q$-difference equations for the colored Jones polynomials of knots.
\begin{equation}
\hat{A}_K(\hat{l},\hat{m};q)J_n(K;q)=0
\end{equation}
where the actions of ...
- 3,474
8
votes
1
answer
1k
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:
$\frac{1}...
- 2,869