The Kauffman bracket skein module of a twist knot exterior

Bullock, Doug; Faro, Walter Lo

doi:10.2140/agt.2005.5.107

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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 2000

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

Volume 5, issue 1 (2005)