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December 2019 Psyquandles, Singular Knots and Pseudoknots
Sam NELSON, Natsumi OYAMAGUCHI, Radmila SAZDANOVIC
Tokyo J. Math. 42(2): 405-429 (December 2019). DOI: 10.3836/tjm/1502179287

Abstract

We generalize the notion of biquandles to psyquandles and use these to define invariants of oriented singular links and pseudolinks. In addition to psyquandle counting invariants, we introduce Alexander psyquandles and corresponding invariants such as Alexander psyquandle polynomials and Alexander-Gröbner psyquandle invariants of oriented singular knots and links. We consider the relationship between Alexander psyquandle colorings of pseudolinks and $p$-colorings of pseudolinks. As a special case we define a generalization of the Alexander polynomial for oriented singular links and pseudolinks we call the Jablan polynomial and compute the invariant for all pseudoknots with up to five crossings and all 2-bouquet graphs with up to 6 classical crossings.

Citation

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Sam NELSON. Natsumi OYAMAGUCHI. Radmila SAZDANOVIC. "Psyquandles, Singular Knots and Pseudoknots." Tokyo J. Math. 42 (2) 405 - 429, December 2019. https://doi.org/10.3836/tjm/1502179287

Information

Published: December 2019
First available in Project Euclid: 29 October 2018

zbMATH: 07209627
MathSciNet: MR4106586
Digital Object Identifier: 10.3836/tjm/1502179287

Subjects:
Primary: 57M27
Secondary: 57M25

Rights: Copyright © 2019 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
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Vol.42 • No. 2 • December 2019
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