Colloquia — Summer 2009
Wednesday, May 20, 2009
Quandle homology and its geometric applications in knot theory
University of Louisiana at Lafayette
A quandle is an algebraic structure whose axioms model the Reidemeister moves in classical knot theory. Quandles are of interest to topologists since the knot quandle is a classifying invariant of knots up to orientation-reversing homeomorphisms of topological pairs. Finite quandles are of particular interest as a source of computable invariants that nicely reflect various geometric properties of knots and links.
The talk will be focused on the homology theory of quandles. We will describe our attempts to understand the structure and patterns appearing in these homology groups. We will also discuss some of its geometric applications.