UIC Graduate Student Seminar

Friday August 24
3:00 pm
636 SEO

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.