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July 2019 Virtual link and knot invariants from non-abelian Yang-Baxter 2-cocycle pairs
Marco A. Farinati, Juliana García Galofre
Osaka J. Math. 56(3): 525-547 (July 2019).

Abstract

Given a set $X$, we provide the algebraic counterpart of the (mixed) Reidemeister moves for virtual knots and links, with semi-arcs labeled by $X$: we define (commutative and noncommutative) invariants with values in groups, using ``2-cocycles", and we also introduce a universal group $U_{nc}^{fg}(X)$ and functions $\pi_f, \pi_g\colon X\times X\to U_{nc}^{fg}(X)$ governing all 2-cocycles in $X$. We exhibit examples of computations -of the group and their invariants- achieved using GAP [7].

Citation

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Marco A. Farinati. Juliana García Galofre. "Virtual link and knot invariants from non-abelian Yang-Baxter 2-cocycle pairs." Osaka J. Math. 56 (3) 525 - 547, July 2019.

Information

Published: July 2019
First available in Project Euclid: 16 July 2019

zbMATH: 07108029
MathSciNet: MR3982044

Subjects:
Primary: 57M25, 57M27

Rights: Copyright © 2019 Osaka University and Osaka City University, Departments of Mathematics

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Vol.56 • No. 3 • July 2019
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