AN INVARIANT FOR SINGULAR KNOTS

DOI10.1142/S0218216509007324zbMath1188.57010arXiv0905.3665OpenAlexW2002043678MaRDI QIDQ3397603

Sofia Lambropoulou, Jesús Juyumaya

Publication date: 22 September 2009

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.3665

zbMATH Keywords

singular knotsYokonuma-Hecke algebrasingular braidsMarkov trace

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Braid groups; Artin groups (20F36)

Related Items (27)

Cocycle invariants and oriented singular knots ⋮ An isomorphism theorem for Yokonuma-Hecke algebras and applications to link invariants ⋮ Involutory biquandles and singular knots and links ⋮ Singquandles, psyquandles, and singular knots: A survey ⋮ Tied links and invariants for singular links ⋮ A framization of the Hecke algebra of type B ⋮ A non-classification result for wild knots ⋮ Singquandle shadows and singular knot invariants ⋮ \(p\)-adic framed braids. II ⋮ Singular knots and involutive quandles ⋮ Classical link invariants from the framizations of the Iwahori–Hecke algebra and the Temperley–Lieb algebra of type A ⋮ Representation theory of the Yokonuma-Hecke algebra. ⋮ THE YOKONUMA–HECKE ALGEBRAS AND THE HOMFLYPT POLYNOMIAL ⋮ Generating sets of Reidemeister moves of oriented singular links and quandles ⋮ Representation theory and an isomorphism theorem for the framisation of the Temperley-Lieb algebra ⋮ Foundations of the Colored Jones Polynomial of singular knots ⋮ An Adelic Extension of the Jones Polynomial ⋮ Framization of a Temperley-Lieb algebra of type \(\mathtt{B}\) ⋮ New skein invariants of links ⋮ A new two-variable generalization of the Jones polynomial ⋮ On 3-strand singular pure braid group ⋮ On the link invariants from the Yokonuma–Hecke algebras ⋮ Enabling computations for link invariants coming from the Yokonuma–Hecke algebras ⋮ Skein invariants of links and their state sum models ⋮ Polynomial invariants of singular knots and links ⋮ Tied links in the solid torus ⋮ Determination of the representations and a basis for the Yokonuma-Temperley-Lieb algebra.

Cites Work

• \(p\)-adic framed braids
• Hecke algebra representations of braid groups and link polynomials
• Link invariants of finite type and perturbation theory
• THE SINGULAR BRAID MONOID EMBEDS IN A GROUP
• LINK POLYNOMIALS AND A GRAPHICAL CALCULUS
• Singular Braids and Markov's Theorem
• MARKOV TRACE ON THE YOKONUMA–HECKE ALGEBRA
• New points of view in knot theory
• L-MOVES AND MARKOV THEOREMS

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