Introduction to knot theory

Unterrichtssprache: Englisch

Testatbedingung: keine

Exercises and course material: click here!

Note: The exercise sheets are an integral part of the course and will be part of the exam.

Office hours during the holidays: Tuesday the 3rd, 10th and 24th of January, 14:00. Please let me know per mail if you are coming and what you want to discuss.

Contents

Definition of a knot and of equivalent knots. Definition of a knot invariant and some simple examples. Various operations on knots. Knot polynomials (Jones and Alexander). Alternating knots. A short review of surfaces and then Seifert surfaces and the Seifert matrix.

Documentation

There are no official notes

Literature

The course will closely follow:

• J.Roberts, Knots Knotes , unpublished lecture notes

For further reading the following books are recommended - an extensive bibliography will be handed out in the course:

• Colin C.Adams, The Knot book
• NEW: M.Akveld, A.Jobbings, Knots unravelled (suitable for high school)
• M.Akveld, Knoten in der Mathematik (suitable for high school)
• G.Burde, H.Zieschang, Knots
• W.B.R.Lickorish, An Introduction to Knot Theory
• C.Livingston, Knot theory
• K.Murasugi, Knot Theory & Its Applications (used for the chapter about the Seifert matrix and the Alexander polynomial)

This paper is an interesting proof of the classification of surfaces due to Conway.