Due to coronavirus, this course will be taught entirely online. The course is structured as a reading module with weekly exercises and discussion sessions on Zoom. During discussion sessions, students will present their solutions to the previous week's problems and the lecturer will guide discussion surrounding those problems. After the discussion session, solutions to the problems will be uploaded to this webpage.
Solutions to exercises should be scanned/photographed (with a resolution high enough that the text is legible) and then emailed directly to the lecturer. They will be marked electronically and returned.
Course entry on ekvv.
| Reading Deadline | Pages | Topic |
|---|---|---|
| 1/5 | 3 - 7 | Basic of knots and links, Reidemeister moves |
| 8/5 | 7 - 10 | 3-colourability |
| 15/5 | 10 - 15 | Crossing number, knot composition, alternating knots |
| 22/5 | 15 - 18 | Writhe, linking number |
| 29/5 | 18 - 26 | Knot polynomials |
| 5/6 | 18 - 26 | More knot polynomials |
| 12/6 | 27 - 33 | Topological surfaces, Euler characteristic, genus |
| 19/6 | 33 - 36 | Surfaces with boundary |
| 26/6 | 36 - 40 | Seifert surfaces, knot genus |
| 3/7 | 1 - 15 (A study of Braids) | Introduction to braids and the braid group |
| 10/7 | 15 - 19, 24 - 28 (A Study of Braids) | Artin presentation of braids and basic properties of braid groups |
| 17/7 | 146 - 149, 163 - 166 + this video | Alexander's Theorem and Markov's Theorem |
The files below are password protected. The password will be distributed during our first Zoom session.
Lecture Notes