The Kauffman bracket skein module of two-bridge links

Le, Thang; Tran, Anh

doi:10.1090/S0002-9939-2013-11835-6

The Kauffman bracket skein module of two-bridge links
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by Thang T. Q. Le and Anh T. Tran

Proc. Amer. Math. Soc. 142 (2014), 1045-1056

DOI: https://doi.org/10.1090/S0002-9939-2013-11835-6

Published electronically: December 12, 2013

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Abstract:

We calculate the Kauffman bracket skein module (KBSM) of the complement of all two-bridge links. For a two-bridge link, we show that the KBSM of its complement is free over the ring $\mathbb {C}[t^{\pm 1}]$ and when reducing $t=-1$, it is isomorphic to the ring of regular functions on the character variety of the link group.

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