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Results tagged with quantum-topology
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user 17644
Finite-type (Vassiliev) invariants, quantum invariants, and perturbative invariants of knotted objects and of manifolds.
2
votes
0
answers
102
views
Mutant pairs distinguished by [2,1]-colored HOMFLY polynomials
Morton and Cromwell showed that the famous mutant pair, Kinoshita-Terasaka and Conway knots, can be distinguished by HOMFLY polynomials colored by [2,1] Young diagram. Are there any other mutant pairs …
- 2,273
7
votes
Accepted
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 …
- 2,273
5
votes
0
answers
346
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. …
- 2,273
4
votes
S-matrix for the HOMFLY/Hecke category
The $S$-matrix is given by
\begin{equation}
\frac{S_{ij}}{S_{00}}=S_{R_i}(q^{\rho})S_{R_j}(q^{\rho+R_i})
\end{equation}
where $S_{R}(x_1,\cdots,x_N)$ is the Schur polynomial with highest weight $R$, …
- 2,273