6
votes
2answers
113 views

On trivalent spines of surfaces

Let $\Sigma$ be a surface with non-empty boundary labelled by finitely many points $x_i$. For our purposes a spine $s$ for $\Sigma$ is a uni-trivalent graph embedded in $\Sigma$ whose 1-vertices are ...
7
votes
1answer
286 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 ...
1
vote
1answer
129 views

Skein Modules on closed 3-manifolds

Hi all! Why are skein modules 1-dimensional on closed 3-manifolds? The result seems clear on closed manifolds with vanishing first Betti number (e.g. $S^3$), but I don't see how to prove it for, say, ...
4
votes
1answer
209 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). ...