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arXiv · 2009.07950

Cocycle Invariants and Oriented Singular Knots

Jose Ceniceros·Indu R. Churchill·Mohamed Elhamdadi·Mustafa Hajij
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Abstract

We extend the quandle cocycle invariant to oriented singular knots and links using algebraic structures called \emph{oriented singquandles} and assigning weight functions at both regular and singular crossings. This invariant coincides with the classical cocycle invariant for classical knots but provides extra information about singular knots and links. The new invariant distinguishes the singular granny knot from the singular square knot.

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Jose Ceniceros, Indu R. Churchill, Mohamed Elhamdadi, Mustafa Hajij. 2020-09-16. Cocycle Invariants and Oriented Singular Knots. https://arxiv.org/abs/2009.07950

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