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Singquandle shadows and singular knot invariants

Published online by Cambridge University Press:  24 September 2021

Jose Ceniceros ,
Indu R. Churchill  and
Mohamed Elhamdadi
Jose Ceniceros
Affiliation:
Department of Mathematics and Statistics, Hamilton College, College Hill Rd., NY13323, USA e-mail: [email protected]
Indu R. Churchill
Affiliation:
Mathematics Department, State University of New York at Oswego, 7060 NY-104, NY13126, USA e-mail: [email protected]
Mohamed Elhamdadi*
Affiliation:
Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler Ave., FL33620, USA
*
e-mail: [email protected]
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Abstract

We introduce shadow structures for singular knot theory. Precisely, we define two invariants of singular knots and links. First, we introduce a notion of action of a singquandle on a set to define a shadow counting invariant of singular links which generalize the classical shadow colorings of knots by quandles. We then define a shadow polynomial invariant for shadow structures. Lastly, we enhance the shadow counting invariant by combining both the shadow counting invariant and the shadow polynomial invariant. Explicit examples of computations are given.

Keywords

Quandle polynomialsingular knots and linkssingquandle polynomial
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 3 , September 2022 , pp. 770 - 787
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Copyright
© Canadian Mathematical Society 2021

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