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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Kauffman bracket skein module of two-bridge links


Authors: Thang T. Q. Le and Anh T. Tran
Journal: Proc. Amer. Math. Soc. 142 (2014), 1045-1056
MSC (2010): Primary 57N10; Secondary 57M25
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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Additional Information

Thang T. Q. Le
Affiliation: School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332
Email: letu@math.gatech.edu

Anh T. Tran
Affiliation: School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332
Address at time of publication: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210
Email: tran.350@osu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11835-6
PII: S 0002-9939(2013)11835-6
Keywords: Skein module, character variety, two-bridge link
Received by editor(s): November 7, 2011
Received by editor(s) in revised form: April 17, 2012
Published electronically: December 12, 2013
Additional Notes: The first author was supported in part by the National Science Foundation
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.