Affiliation:
1. Jordan University of Science and Technology , Irbid , Jordan
Abstract
Abstract
We define a new algebraic structure for singular knots and links. It extends the notion of a bikei (or involutory biquandle) from regular knots and links to singular knots and links. We call this structure a singbikei. This structure results from the generalized Reidemeister moves representing singular isotopy. We give several examples on singbikei and we use singbikei to distinguish several singular knots and links.
Reference19 articles.
1. Birman JS., New points of view in knot theory, Bulletin of the American Mathematical Society, 1993, 28, 253-87.
2. Birman JS., Lin XS., Knot polynomials and Vassiliev’s invariants, Inventiones mathematicae, 1993, 111, 225-70.
3. Vassiliev VA., Cohomology of knot spaces, Theory of singularities and its applications, 1990, 1, 23-69.
4. Bataineh K., Elhamdadi M., Hajij M., The colored Jones polynomial of singular knots, New York J. Math., 2016, 22, 1439-56.
5. Fiedler T., The Jones and Alexander polynomials for singular links, Journal of Knot Theory and Its Ramifications, 2010, 19, 859-66.