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Three
approaches to a bracket polynomial for singular links
Carmen Caprau, Alex Chichester and Patrick Chu
Vol. 10 (2017), No. 2, 197–218
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Abstract |
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In this paper we extend the Kauffman bracket to singular links. Specifically, we define a polynomial invariant for singular links, and in doing this, we consider three approaches to our extended Kauffman bracket polynomial: (1) using skein relations involving singular link diagrams, (2) using representations of the singular braid monoid, (3) via a Yang–Baxter state model. We also study some properties of the extended Kauffman bracket. |
Keywords
Kauffman bracket, invariants for knots and links, singular
braids and links, Yang–Baxter equation
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
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Milestones
Received: 29 June 2014
Revised: 28 January 2015
Accepted: 17 August 2015
Published: 10 November 2016
Communicated by Jim Hoste
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Authors |
| Carmen Caprau | |
| Department of Mathematics California State University, Fresno 5245 N. Backer Avenue M/S PB108 Fresno, CA 93740-8001 United States |
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| Alex Chichester | |
| Department of Mathematics SUNY Geneseo Geneseo, NY 14454 United States |
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| Patrick Chu | |
| Department of Mathematics Rice University Houston, TX 77005 United States |
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