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The Kauffman bracket skein module of a twist knot exterior

Doug Bullock and Walter Lo Faro

Algebraic & Geometric Topology 5 (2005) 107–118

DOI: 10.2140/agt.2005.5.107

arXiv: math.QA/0402102
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
Mathematical Subject Classification

Primary: 57M27

Secondary: 57M99
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Publication

Received: 2 February 2004
Revised: 3 February 2005
Accepted: 6 June 2004
Published: 7 February 2005
Authors
Doug Bullock
Department of Mathematics
Boise State University
Boise ID 83725
USA
Walter Lo Faro
Department of Mathematics
University of Wisconsin
Stevens Point WI 54481
USA