In this paper, we deal with the notion of singquandles introduced in [I. R. U. Churchill, M. Elhamdadi, M. Hajij and S. Nelson, Singular knots and involutive quandles, J. Knot Theory Ramifications 26(14) (2017) 1750099]. This is an algebraic structure that naturally axiomatizes Reidemeister moves for singular links, similarly to what happens for ordinary links and quandles. 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).

Bonatto, M., Cattabriga, A. (2022). On the axioms of singquandles. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 31(13), 22594-22610 [10.1142/S0218216522500948].

On the axioms of singquandles

Bonatto, M.;Cattabriga, A.
2022

Abstract

In this paper, we deal with the notion of singquandles introduced in [I. R. U. Churchill, M. Elhamdadi, M. Hajij and S. Nelson, Singular knots and involutive quandles, J. Knot Theory Ramifications 26(14) (2017) 1750099]. This is an algebraic structure that naturally axiomatizes Reidemeister moves for singular links, similarly to what happens for ordinary links and quandles. 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).
2022
Bonatto, M., Cattabriga, A. (2022). On the axioms of singquandles. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 31(13), 22594-22610 [10.1142/S0218216522500948].
Bonatto, M.; Cattabriga, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/917659
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