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Kauffman bracket skein module of the $(3,3,3,3)$-pretzel link exterior
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abstract
We show that the Kauffman bracket skein module of the $(3,3,3,3)$-pretzel link exterior over $\mathbb{Q}(q^{\frac{1}{2}})$ is not finitely generated as a module over $\mathbb{Q}(q^{\frac{1}{2}})[t_1,t_2]$, where $t_1,t_2$ are the meridians of two components. This disproves a finiteness conjecture of Detcherry proposed in 2021.
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Cited by 1 Pith paper
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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.
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