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2016 Singular links and Yang-Baxter state models
Carmen Caprau, Tsutomu Okano, Danny Orton
Rocky Mountain J. Math. 46(6): 1867-1898 (2016). DOI: 10.1216/RMJ-2016-46-6-1867


We employ a solution of the Yang-Baxter equation to construct invariants for knot-like objects. Speci\-fically, we consider a Yang-Baxter state model for the {\rm sl($n$)} polynomial of classical links and extend it to oriented singular links and balanced oriented 4-valent knotted graphs with rigid vertices. We also define a representation of the singular braid monoid into a matrix algebra and seek conditions for further extending the invariant to contain topological knotted graphs. In addition, we show that the resulting Yang-Baxter-type invariant for singular links yields a version of the Murakami-Ohtsuki-Yamada state model for the {\rm sl($n$)} polynomial for classical links.


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Carmen Caprau. Tsutomu Okano. Danny Orton. "Singular links and Yang-Baxter state models." Rocky Mountain J. Math. 46 (6) 1867 - 1898, 2016.


Published: 2016
First available in Project Euclid: 4 January 2017

zbMATH: 1359.57004
MathSciNet: MR3591264
Digital Object Identifier: 10.1216/RMJ-2016-46-6-1867

Primary: 57M15 , 57M27

Keywords: [! \rm !]sl($n$) polynomial , Graphs , invariants for knots and links , singular braids and links , Yang-Baxter equation

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium


Vol.46 • No. 6 • 2016
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