Vol. 10, No. 2, 2017

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Three approaches to a bracket polynomial for singular links

Carmen Caprau, Alex Chichester and Patrick Chu

Vol. 10 (2017), No. 2, 197–218
Abstract

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
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Milestones
Received: 29 June 2014
Revised: 28 January 2015
Accepted: 17 August 2015
Published: 10 November 2016

Communicated by Jim Hoste
Authors
Carmen Caprau
Department of Mathematics
California State University, Fresno
5245 N. Backer Avenue M/S PB108
Fresno, CA 93740-8001
United States
Alex Chichester
Department of Mathematics
SUNY Geneseo
Geneseo, NY 14454
United States
Patrick Chu
Department of Mathematics
Rice University
Houston, TX 77005
United States