University of Georgia
Mathematics Department Colloquium
Prof. Scott Carter
University of South Alabama
Nov 16, 2000
Quandle Homology and Abstract Knot Diagrams
Abstract:
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.
Another example is the numbers (0,1,2) under the operation i*j=2j-i.
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.