Algebraic and Geometric Topology 5 (2005), paper no. 6, pages 107-118.

The Kauffman bracket skein module of a twist knot exterior

Doug Bullock, Walter Lo Faro

Abstract. We compute the Kauffman bracket skein module of the complement of a twist knot, finding that it is free and infinite dimensional. The basis consists of cables of a two-component link, one component of which is a meridian of the knot. The cabling of the meridian can be arbitrarily large while the cabling of the other component is limited to the number of twists.

Keywords. Knot, link, skein module, Kauffman bracket

AMS subject classification. Primary: 57M27. Secondary: 57M99.

DOI: 10.2140/agt.2005.5.107

E-print: arXiv:math.QA/0402102

Submitted: 2 February 2004. (Revised: 3 February 2005.) Accepted: 6 June 2004. Published: 7 February 2005.

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Doug Bullock, Walter Lo Faro
Department of Math, Boise State University
Boise, ID 83725, USA
and
Department of Math, University of Wisconsin
Stevens Point, WI 54481, USA
Email: bullock@math.boisestate.edu, Walter.LoFaro@uwsp.edu

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