The paper gives a monomial basis and a finite presentation for the Kauffman bracket skein algebra of the 4-holed disk over Z[q^{±1/2}], extending previous coefficient fields and adding a character variety freeness theorem.
Kauffman bracket skein module of two families of Seifert manifolds
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abstract
We compute the Kauffman bracket skein modules of Seifert manifolds $\Sigma_{0,1}((k_1,1),(k_2,1))$ and $\Sigma_{0,0}((k_1,1),(k_2,1),(k_3,1))$ by providing presentations of them. From the obtained presentations, we show that the Kauffman bracket skein modules of $\Sigma_{0,1}((k_1,1),(k_2,1))$ are free with infinitely many generators when $k_1,k_2\ge 1$ and that of $\Sigma_{0,0}((k_1,1),(k_2,1),(k_3,1))$ are finitely generated when $k_1,k_2,k_3 \ge 2$. We also show that the empty link in either case is not trivial.
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Kauffman bracket skein algebra of the 4-holed disk
The paper gives a monomial basis and a finite presentation for the Kauffman bracket skein algebra of the 4-holed disk over Z[q^{±1/2}], extending previous coefficient fields and adding a character variety freeness theorem.