Topology and groups

Module overview

What is Topology and Groups about?

Topology and Groups is about the interaction between topology and algebra, via an object called the fundamental group. This allows you to translate certain topological problems into algebra (and solve them) and vice versa.

We will:

Flipped lectures

This module will be different from most modules you will have taken at UCL. Instead of me standing up and lecturing for 3 hours a week, I have pre-recorded your lectures and put them online (together with lecture notes for each lecture). Your weekly homework will be to watch the relevant videos for the next lecture and to do any of the (hopefully short) associated pre-class questions (as well as finishing off any of the work you started but didn't finish in-class).

Before each in-class session, you will need to prepare by:

You can see which videos are required for each in-class session by referring to the week-by-week plan below.

In class, we will:


I will assume you are familiar with:



Some weeks will involve more videos than others, averaging about an 1.5 hours per week. Of course, it will take you longer than the stated time to watch and absorb each video, as you may need to pause and think, make coffee, rewind, etc. How you fit this in is up to you, as long as you have watched the videos/read the notes before the corresponding session. If you find it easier/quicker to just read the notes (referring only to the videos when you get stuck) that's fine: we all learn in different ways.

Week-by-week plan

Each week there is a 2-hour session on Monday 12--2 and a 1-hour session on Thursday 9-10. Below I indicate what videos we will be focusing on in which sessions, along with the total watching time (to help you plan your lives). Each link is to a page with an embedded video (usually 15-20 minutes long) along with notes and pre-class questions for the video.

In preparation for each session, I expect you to have either watched the video or read the notes (or both) and to have thought about the pre-class questions enough that you would happily discuss your thoughts on each question with the class (even if you haven't completely figured it out).

Week 1 (44m 34s)

Week 2 (1h 16m 5s)

Week 3 (1h 37m 1s)

Week 4 (1h 25m 31s)

Week 5 (1h 42m 4s)

Reading week (41m 36s)

No sessions, you have the chance to watch the (nonexaminable) proof of Van Kampen's theorem 5.04 (41.36) at your leisure.

Week 6 (1h 1m 15s)

Week 7 (1h 25m 9s)

Week 8 (1h 31m 9s)

Week 9 (1h 6m 46s)

Week 10 (36m 19s)

Index of all video lectures

Each page below contains:

The notes are annotated with times (these annotations should look like (8.30)) which indicate whereabouts in the video you can see that section of the notes. I have also indicated the length of the videos below similarly.


Solutions to all worksheets.