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An Introduction to Quandles, Their Homology, and Applications
by
J. Scott Carter
University of South Alabama
Abstract. The idea of a set with a binary operation that is self-distributive goes back to Takasaki (1942/43). In the early 1980s, Matveev and Joyce independently developed the axioms that we now call a quandle. They associated a quandle to the complement of a knot, and they showed that the knot quandle characterized the complement up to orientation reversing homeomorphism. Their construction is interesting to consider from the point of view of quandle 2-cocycles.
Quandle will be defined and exemplified with some nice geometric examples. Quandle (co)homology will be sketched, and some of the applications of quandle cocycle invariants that have been discovered by a variety of authors will be highlighted.
Date received: November 15, 2010
Copyright © 2010 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 # cbbr-14.