Title: Knots and Links with Finite n-Quandles
Speaker: Alissa Crans (Loyola Marymount University)
Abstract: A quandle is a set equipped with two binary operations satisfying axioms that capture the essential properties of the operations of conjugation in a group and algebraically encode the three Reidemeister moves from classical knot theory. Thus, quandles are a fruitful source of applications to knots and knotted surfaces; in particular they provide a complete invariant of knots. An n-quandle is a quandle that, roughly speaking, satisfies the additional axiom that applying the quandle operation n times with the same element is trivial. We will consider the collection of knots and links having finite n-quandles, describe many of these quandles, and identify their automorphism, inner automorphism, and transvection groups. This is joint work with Jim Hoste, Blake Mellor and Patrick Shanahan.
Seminar URL: https://www.coreyjonesmath.com/qaqt-seminar-osu
