Moscow Mathematical Journal

Volume 16, Issue 3, July–September 2016 pp. 397–431.

Markov Trace on the Algebra of Braids and Ties

Authors: Francesca Aicardi (1) and Jesús Juyumaya (2)
Author institution:(1) The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera, 11, 34151 Trieste, Italy
(2) Instituto de Matemáticas, Universidad de Valparaíso, Gran Bretaña 1111, Valparaíso, Chile

Summary:

We prove that the so-called algebra of braids and ties supports a Markov trace. Further, by using this trace in the Jones’ recipe, we define invariant polynomials for classical knots and singular knots. Our invariants have three parameters. The invariant of classical knots is an extension of the Homflypt polynomial and the invariant of singular knots is an extension of an invariant of singular knots previously defined by S. Lambropoulou and the second author.

2010 Math. Subj. Class. 57M25, 20C08, 20F36.

Keywords: Markov trace, algebra of diagrams, knots invariants.

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