Singquandle Shadows and Singular knot Invariants
Geometric Topology
2021-01-22 v1 Quantum Algebra
Rings and Algebras
Abstract
We introduce shadow structures for singular knot theory. Precisely, we define \emph{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
Cite
@article{arxiv.2101.08775,
title = {Singquandle Shadows and Singular knot Invariants},
author = {Jose Ceniceros and Indu R. Churchill and Mohamed Elhamdadi},
journal= {arXiv preprint arXiv:2101.08775},
year = {2021}
}
Comments
17 pages, 11 figures. Comments are welcome