Overview
Description
Knot Theory is the study of knots and links in 3-space. It is a fundamental part of low-dimensional topology, but knots have found applications in biology, chemistry, physics and beyond. The classification of knots is the theory’s main goal, a hard and unsolved problem, chiefly studied by means of knot invariants. This class is an introduction to knot theory, and will present many examples of knots, and study a host of knot invariants: The Alexander and Jones polynomials, knot genera, etc.
Units
Lecture3
Catalog Details
Offering
Offered: Every Fall - Odd Years
Terms
fall
Attributes
Standard
Learning Outcomes
- calculate the Alexander-Conway, Jones and HOMFLYPT polynomial of a knot/link using skein relations.
- describe and classify the certain families of knots, such as torus knots and twist knots.
- use a Seifert surface of a knot/link to compute its signature, determinant and linking form.
- calculate the Wirtinger presentation of the knot group.