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Knot colorings by quandles and their animations
by
Masahico Saito
University of South Florida
Coauthors: W. Edwin Clark
A Fox coloring of a knot diagram is defined by assigning integers modulo n to arcs of the diagram with a certain condition at every crossing. The number of colorings is independent of choice of a diagram, and is a knot invariant. This idea leads to a concept of an algebraic system called quandles, that have self-distributive binary operations with a few other conditions. Knot colorings are defined with quandles and yield knot invariants. This was further generalized to knot invariants called quandle cocycle invariants, incorporating ideas from quantum knot invariants and group cohomology. After a review of these concepts, we consider quandle cocycle invariants with matrix groups. A continuous family of knot colorings is represented by animations of polygons moving on the sphere. These animations will be presented.
Date received: December 2, 2016
Copyright © 2016 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbnq-35.