7
votes
1answer
288 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
1answer
212 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). ...
5
votes
1answer
533 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 ...
15
votes
4answers
1k 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: ...