Singular Knots and Involutive Quandles

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.

arXiv comment10 pages; v5 removes incorrect examples from Section 5 and adds a new example, incorporating Errata for published version