On the axioms of singquandles

Marco Bonatto; Alessia Cattabriga

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arXiv · 2107.04801

On the axioms of singquandles

Marco Bonatto·Alessia Cattabriga

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Abstract

In this paper we deal with the notion of singquandles introduced in Indu R. U. Churchill, Mohamed Elhamdadi, Mustafa Hajij, and Sam Nelson, Singular knots and involutive quandles, Journal of Knot Theory and Its Ramifications 26 (2017), no. 14. This is an algebraic structure that naturally axiomatizes Reidemeister moves for singular links, similarly to what happens for ordinary links and quandle structure. We present a new axiomatization that shows different algebraic aspects and simplifies applications. We also reformulate and simplify the axioms for affine singquandles (in particular in the idempotent case).

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Marco Bonatto, Alessia Cattabriga. 2021-07-10. On the axioms of singquandles. https://arxiv.org/abs/2107.04801

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