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Senior Project Presentation Shannan Allyn

Summary: Senior Project Presentation
Shannan Allyn
Title: Quandle coloring of knots
Advisor: Dr. Mohamed Ait Nouh
A quandle is an algebraic concept derived from Reidmeister moves in Knot
Theory. A quandle is defined as a set Q paired with a binary operation satisfying
three axioms: For all x, y, z Q:
(1) x x = x.
(2) There exists a unique z Q : z y = x, and
(3)(x y) z = (x z) (y z).
Quandle theory is a relatively new subject in abstract algebra which has appli-
cations to various areas of topology. Readers who are familiar with abstract algebra
should think of quandle theory as analogous to group theory. In fact, a form of
quandle now called an "involutory quandle" was described in Japan (called "kei")
as far back as 1942!. Variants on the quandle idea have been studied by Conway
(wracks), Brieskorn (automorphic sets), Matveev (distributive groupoids), Kauff-
man (crystals), Fenn and Rourke (racks), though the current terminology is due to
David Joyce, who coined the word "quandle" in his 1980 doctoral dissertation. In
this talk, I will give examples of important quandles and discuss three facts:
(1) How quandles are derived from Knot theory via Reidmeister moves.


Source: Ait Nouh, Mohamed - Mathematics Department, California State University Channel Islands


Collections: Mathematics