This article is cited in 23 papers

Markov trace on the algebra of braids and ties

Francesca Aicardi^a, Jesús Juyumaya<sup>b

a</sup> The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera, 11, 34151 Trieste, Italy
^b Instituto de Matemáaticas, Universidad de Valparaíso, Gran Bretaña 1111, Valparaíso, Chile

Abstract: 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.

Key words and phrases: Markov trace, algebra of diagrams, knots invariants.

MSC: 57M25, 20C08, 20F36

Received: October 7, 2014; in revised form January 13, 2016

Language: English

DOI: 10.17323/1609-4514-2016-16-3-397-431

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