Generating Sets of Reidemeister Moves of Oriented Singular Links and Quandles
Generating sets of Reidemeister moves, quandles, oriented singular knots
Digital Object Identifier (DOI)
We give a generating set of the generalized Reidemeister moves for oriented singular links. We then introduce an algebraic structure arising from the axiomatization of Reidemeister moves on oriented singular knots. We give some examples, including some non-isomorphic families of such structures over non-abelian groups. We show that the set of colorings of a singular knot by this new structure is an invariant of oriented singular knots and use it to distinguish some singular links.
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Citation / Publisher Attribution
Journal of Knot Theory and Its Ramifications, v. 27, issue 14, art. 1850064
Scholar Commons Citation
Bataineh, Khaled; Elhamdadi, Mohamed; Hajij, Mustafa; and Youmans, William, "Generating Sets of Reidemeister Moves of Oriented Singular Links and Quandles" (2018). Mathematics and Statistics Faculty Publications. 99.