Singular Links and Yang-Baxter State Models

Carmen Caprau; Tsutomu Okano; Danny Orton

doi:10.1216/rmj-2016-46-6-1867

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arXiv · 1406.3853

Singular Links and Yang-Baxter State Models

Carmen Caprau·Tsutomu Okano·Danny Orton

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Abstract

We employ a solution of the Yang-Baxter equation to construct invariants for knot-like objects. Specifically, we consider a Yang-Baxter state model for the 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 extending further 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 sl(n) polynomial for classical links.

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BibTeX RIS

Carmen Caprau, Tsutomu Okano, Danny Orton. 2014-06-15. Singular Links and Yang-Baxter State Models. https://doi.org/10.1216/rmj-2016-46-6-1867

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