Quantum Topology Seminar
Louis H Kauffman
UIC
Introduction of Quandles
Abstract: We will continue the introduction to quandles from the last meeting. This talk is self-contained and will review
the previous talk quickly. An (involuntary) quandle is an algebraic structure Q with one binary operation satisfying
a*a=a , (a*b)*b = a, (a*b)*c = (a*c)*(b*c) for all a,b,c in Q. Quandles can be used to make invariants of knots
and links. Here is an algebraic example: Let G be a group with multiplication ab. Define a*b = ba^{-1}b and verify
that this gives a quandle structure on G. This construction is related to the fundamental group of the
double branched covering of a knot or link in the three sphere, and can be used to define a quandle invariant of
knots that detects the unknot.
Thursday January 23, 2020 at 3:00 PM in 1227 SEO