Singular Knots and Involutive Quandles
Indu R. U. Churchill, M. Elhamdadi, M. Hajij, Sam Nelson
TL;DR
This paper introduces algebraic structures derived from generalized Reidemeister moves in singular knot theory, demonstrating their effectiveness in classifying and distinguishing singular knots and links.
Contribution
It defines new algebraic structures from singular knot moves and proves their invariance, providing tools to distinguish complex singular knots and links.
Findings
Set of colorings by these structures is an invariant of singular links
Successfully distinguished several singular knots and links
Provides examples of the algebraic structures
Abstract
The aim of this paper is to define certain algebraic structures coming from generalized Reidemeister moves of singular knot theory. We give examples, show that the set of colorings by these algebraic structures is an invariant of singular links. As an application we distinguish several singular knots and links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Mathematics and Applications