Shalen Abstract UGA Math University of Georgia Mathematics Department Colloquium Prof. A quandle is a set with a self-distributive binary operation defined. A typical example of a quandle is a group with conjugation as the operation. Quandles were invented to study knots in 3-space.
Every knot has a fundamental quandle.
An elementary knot invariant is the number of ways a finite quandle can color it. There is a homology functor from the category of quandles to the category of Abelian groups. We will define the homology of quandles and present new invariants of classical knots and knotted surfaces that are defined via this homology theory. There are many outstanding question about quandle homology that should be of interest to algebraists and topologists. The talk will be self-contained and I will assume no prior knowledge of knot theory or homology theory.