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Senior Project Presentation Title: Fox coloring of knots
 

Summary: Senior Project Presentation
Erin Bryan
Title: Fox coloring of knots
Advisor: Dr. Mohamed Ait Nouh
Knot theory is an increasingly important field in mathematics, with applications
to biology, chemistry, and physics. It is an exciting field subject for mathematical
research, with many unanswered questions to explore. In particular, knot theorists
have taken interest in the study of coloring of knots as a tool to distinguish between
knots.
This talk provides a gentle introduction to Knot Theory starting from 3-coloring,
a concept named after Ralph Fox, who invented it around 1960 to allow undergrad-
uate students to see that the trefoil knot is non-trivial, and knot theorists generalized
it to Fox p-coloring of knots as a method for obtaining invariants of knots and
links by coloring arcs in a knot diagram.
Amazingly enough, I will show you how the Fox p-coloring and algebra are related
by chronically proving three important features:
(1) it is related to the Jones polynomial, an important knot invariant discovered
by Vaughan Jones in 1985, and
(2) it is equivalent to the coloring with the Dihedral group D2p, and
(3) it is equivalent to solving a linear system...and more !

  

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

 

Collections: Mathematics