Vol. 9, No. 4, 2016

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ISSN: 1944-4184 (e-only)
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Presentations of Roger and Yang's Kauffman bracket arc algebra

Martin Bobb, Dylan Peifer, Stephen Kennedy and Helen Wong

Vol. 9 (2016), No. 4, 689–698
Abstract

The Jones polynomial for knots and links was a breakthrough discovery in the early 1980s. Since then, it’s been generalized in many ways; in particular, by considering knots and links which live in thickened surfaces and by allowing arcs between punctures or marked points on the boundary of the surface. One such generalization was recently introduced by Roger and Yang and has connections with hyperbolic geometry. We provide generators and relations for Roger and Yang’s Kauffman bracket arc algebra of the torus with one puncture and the sphere with three or fewer punctures.

Keywords
Kauffman bracket skein algebra, Kauffman bracket arc algebra
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M50
Milestones
Received: 17 May 2015
Accepted: 31 July 2015
Published: 6 July 2016

Communicated by Colin Adams
Authors
Martin Bobb
Department of Mathematics
University of Texas at Austin
Austin, TX 78712
United States
Dylan Peifer
Department of Mathematics
Cornell University
Ithaca, NY 14853
United States
Stephen Kennedy
Department of Mathematics
Carleton College
Northfield, MN 55057
United States
Helen Wong
Department of Mathematics
Carleton College
Northfield, MN 55057
United States