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401-4575-76L 4 Credits DR , MSC D-MATH

Knot Theory

Lecturers & Examiners: PD Dr. Lukas Lewark
VVZ CR n/a

Last Updated: 2026-06-03 00:07:40

Abstract

Introductory 2h-course on knot theory: the mathematical study of 1-dimensional objects embedded in 3-dimensional spaces.

Objective

The principal objective is to establish knot theory as an independent field with a history going back to Gauss, Kelvin, and Tait. However, we will also discuss connections with other parts of mathematics and a provide a brief outlook on current developments. This course aims to provide hands-on examples of how concepts from topology (such as the fundamental group and surfaces) can be applied to the study of smooth subsets of Euclidian space.

Content

The course starts with an introduction to knots via knot diagrams and some diagram based invariants. Then, we will develop 3D-concepts in knot theory such as the knot group, Seifert surfaces and the Alexander polynomial. We will also touch on connections of knots to 3-dimensional topology. Moreover, quantum invariants such as the Jones polynomial will make an apperance. The course will finish with an outlook on some results from recent years.

Resources

Literature

- An Introduction to Knot Theory, W. B. Raymond Lickorish. - Knots and Links, Dale Rolfsen. - Knots, G. Burde, H. Zieschang, M. Heusener.

General Information

Language
English
Levels
DR , MSC

Examination

Type
session examination
Mode
written 90 minutes
Aids
None
The exam is only offered in the Winter 2027 and Summer 2027 sessions.

Course Components

Type Title Time & Place Hours
lecture Knot Theory No time listed 2 h weekly

Offered In