Introduction to Knot Theory

Exercise classes: Click here for details regarding the exercise classes and exercise sheets .

Literature

Lecture Notes by Justin Roberts

Bibliography

Tentative list of topics to be covered

0. Historical background

1. Informal introduction and outlook

2. Official introduction

3. Simple knot invariants

4. The Jones polynomial

5. Alternating knots

6. Surfaces (an overview)

7. Seifert surfaces

8. The Alexander polynomial

Material from the lecture course

17.02.2015 A table of knots or follow the Link

24.02.2015 A knot whose unknotting number is realised by first increasing the number of crossings. An example of a wild knot , which we will exclude from now on.

17.03.2015 p-colourability is not a complete knot invariant: counterexample

31.03.2015 An example that shows that the number of loops does not necessarily decrease if you increase the number of minuses in a state.

21.04.2015 Properties of the Conway polynomial.

05.05.2015 The classification of surfaces and surfaces with boundary. Seifert's algorithm illustrated on the knot 4_1.

12.05.2015 Compute the Seifert matrix of the following knot bounding this surface .

19.05.2015 Different Seifert surfaces from the same knot diagram. How to get rid of nested circles by changing the knot diagram.

26.05.2015 Some interesting examples regarding the Jones and Alexander polynomial