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).
On the axioms of singquandles / Bonatto, M.; Cattabriga, A.. - In: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS. - ISSN 0218-2165. - ELETTRONICO. - 31:12(2022), pp. 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).| File | Dimensione | Formato | |
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Singquandles_revised2.pdf
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