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18 votes
4 answers
2k views

Who thought that the Alexander polynomial was the only knot invariant of its kind?

I apologize that this is vague, but I'm trying to understand a little bit of the historical context in which the zoo of quantum invariants emerged. For some reason, I have in my head the folklore: ...
Sammy Black's user avatar
  • 1,756
10 votes
1 answer
324 views

Is the quantum $\mathfrak{sl}_3$ invariant stronger than the quantum $\mathfrak{sl}_2$ invariant?

Both the $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$ quantum framed link invariants can be computed using linear skeins. The first being computed using the Kauffman bracket and the second using a similar ...
user530316's user avatar
7 votes
1 answer
853 views

Trace identities and the Kauffman Bracket skein module

Let's consider $K_t(M)$, the Kauffman bracket skein module (see this and this papers) of a three-manifold $M$. When $t=-1$, $K_t(M)$ is easily seen to be isomorphic to the ring of functions on the ...
John Pardon's user avatar
  • 18.7k
6 votes
1 answer
396 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). ...
John Pardon's user avatar
  • 18.7k