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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
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M50
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Milestones
Received: 17 May 2015
Accepted: 31 July 2015
Published: 6 July 2016
Communicated by Colin Adams
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Authors |
| Martin Bobb | |
| Department of Mathematics University of Texas at Austin Austin, TX 78712 United States |
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| Dylan Peifer | |
| Department of Mathematics Cornell University Ithaca, NY 14853 United States |
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| Stephen Kennedy | |
| Department of Mathematics Carleton College Northfield, MN 55057 United States |
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| Helen Wong | |
| Department of Mathematics Carleton College Northfield, MN 55057 United States |
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