MATH 644 - Introduction to Knot Theory

(3 units)

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.

Maximum units a student may earn: 3

Grading Basis: Graded
Units of Lecture: 3
Offered: Every Fall - Odd Years

Student Learning Outcomes
Upon completion of this course, students will be able to:
1. calculate the Alexander-Conway, Jones and HOMFLYPT polynomial of a knot/link using skein relations.
2. describe and classify the certain families of knots, such as torus knots and twist knots.
3. use a Seifert surface of a knot/link to compute its signature, determinant and linking form.
4. calculate the Wirtinger presentation of the knot group.

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