UIC Graduate Student Seminar
Friday August 24
Speaker: Lou Kauffman
Title: Introdcution to Model Theory
Abstract: Knot theory is concerned with the placement problem in topology:
Classify the ways that one space can be embedded in another space.
Classical knot theory considers a simple but highly non-trivial special
case of this problem: Embeddings of a circle or disjoint union of circles
in three dimensional space. These are the knots and links. This talk will
describe how combinatorial group theory can be used to study and indeed to
reformulate algebraically the classification of classical knots and links.
We will show how a non-commutative calculus due to R. Fox can be used to
derive the Alexander polynomial of a knot from its fundamental group.
We will sketch how the study of knots and links is related to the problem
of classifying three dimensional manifolds.