Special Issue for Slavic Jablan; Guest Editors: L. H. Kauffman, R. Sazdanovic and S. LambropoulouNo Access

On the link invariants from the Yokonuma–Hecke algebras

S. Chmutov

Department of Mathematics, Ohio State University, 1680 University Drive, Mansfield, OH 44906, USA

E-mail Address: chmutov@math.ohio-state.edu

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S. Jablan

The Mathematical Institute, Knez Mihailova 36, B.O. Box 367, 11001 Belgrade, Serbia

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K. Karvounis

Institut für Mathematik, Universität Zuricḧ, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

E-mail Address: konstantinos.karvounis@math.uzh.ch

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, and

S. Lambropoulou

Department of Mathematics, National Technical University of Athens, Zografou campus, GR-157 80 Athens, Greece

E-mail Address: sofia@math.ntua.gr

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https://doi.org/10.1142/S0218216516410042Cited by:8 (Source: Crossref)

Abstract

In this paper, we study properties of the Markov trace tr $_{d}$ $_{d}$ and the specialized trace ${tr}_{d, D}$ ${tr}_{d, D}$ on the Yokonuma–Hecke algebras, such as behavior under inversion of a word, connected sums and mirror imaging. We then define invariants for framed, classical and singular links through the trace ${tr}_{d, D}$ ${tr}_{d, D}$ and also invariants for transverse links through the trace tr $_{d}$ $_{d}$ . In order to compare the invariants for classical links with the Homflypt polynomial, we develop computer programs and we evaluate them on several Homflypt-equivalent pairs of knots and links. Our computations lead to the result that these invariants are topologically equivalent to the Homflypt polynomial on knots. However, they do not demonstrate the same behavior on links.

Keywords:

AMSC: 57M27, 57M25, 20F36, 20F38, 20C08

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