## Three approaches to a bracket polynomial for singular links.(English)Zbl 1355.57004

The Kauffman bracket is a polynomial invariant for unoriented knots and links and is defined via a skein relation, i.e., an identity involving knot (or singular link) diagrams that are the same except in a small neighborhood. In the paper under review the authors extend the Kauffman bracket to singular links (Section $$2$$). After that, in Section $$3$$ they study the behavior of the extended Kauffman bracket with respect to disjoint unions, connected sums, and mirror images of singular links. In Section $$4$$ they define a representation of the singular braid monoid into the Temperley-Lieb algebra, and use it to provide a different approach to the extended Kauffman bracket for singular links. Finally, in Section $$5$$ they show how to arrive at the extended Kauffman bracket by interpreting singular link diagrams as abstract tensor diagrams and employing a solution to the Yang-Baxter equation.

### MSC:

 57M25 Knots and links in the $$3$$-sphere (MSC2010) 57M27 Invariants of knots and $$3$$-manifolds (MSC2010)
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