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Moscow Mathematical Journal, 2016, Volume 16, Number 3, Pages 397–431
DOI: https://doi.org/10.17323/1609-4514-2016-16-3-397-431 (Mi mmj605) 		 
This article is cited in 22 scientific papers (total in 22 papers)

Markov trace on the algebra of braids and ties

Francesca Aicardia, Jesús Juyumayab

a 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
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DOI: https://doi.org/10.17323/1609-4514-2016-16-3-397-431
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.
Funding agency Grant number
Fondecyt 1141254
DIUV 1-2011
The second named author was supported in part by Fondecyt 1141254, DIUV No 1–2011 and by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program ‘Education and Lifelong Learning’ of the National Strategic Reference Framework (NSRF) Research Funding Program: THALES: Reinforcement of the interdisciplinary and/or interinstitutional research and innovation.
Received: October 7, 2014; in revised form January 13, 2016
Bibliographic databases:
Document Type: Article
MSC: 57M25, 20C08, 20F36
Language: English
Citation: Francesca Aicardi, Jesús Juyumaya, “Markov trace on the algebra of braids and ties”, Mosc. Math. J., 16:3 (2016), 397–431
Citation in format AMSBIB
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\by Francesca~Aicardi, Jes\'us~Juyumaya
\paper Markov trace on the algebra of braids and ties
\jour Mosc. Math.~J.
\yr 2016
\vol 16
\issue 3
\pages 397--431
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\crossref{https://doi.org/10.17323/1609-4514-2016-16-3-397-431}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3510208}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000391210300001}
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    • This publication is cited in the following 22 articles:
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