The skein algebra of the Borromean rings complement

Go Miura; Sakie Suzuki

doi:10.1142/s0129167x22500495

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arXiv · 2108.02884

The skein algebra of the Borromean rings complement

Go Miura·Sakie Suzuki

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Abstract

The skein algebra of an oriented $3$-manifold is a classical limit of the Kauffman bracket skein module and gives the coordinate ring of the $SL_2(\mathbb{C})$-character variety. In this paper we determine the quotient of a polynomial ring which is isomorphic to the skein algebra of a group with three generators and two relators. As an application, we give an explicit formula for the skein algebra of the Borromean rings complement in $S^3$.

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Go Miura, Sakie Suzuki. 2021-08-05. The skein algebra of the Borromean rings complement. https://doi.org/10.1142/s0129167x22500495

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