MAGIC064 Algebraic Topology
Lecturer: Neil Strickland

Module information

There is a page for this course on the MAGIC website.


Lectures will happen on Tuesdays and Thursdays, from 14:05 to 14:55.

Lecture notes

I will use PDF slides in the lectures. Aditionally, there are three more files of notes:
The construction of singular (co)homology [CSC]
Examples in the (co)homology of spaces [ECS]
Algebraic theory of abelian groups [ATAG]

We will work through the highlights of [CSC], skipping some details. This will define the cohomology ring \(H^*(X)\) of a topological space \(X\), and prove some key properties (the Eilenberg-Steenrod axioms). This will rely on some material from [ATAG], which we will also review. After proving the Eilenberg-Steenrod axioms, we will be able to use them to calculate \(H^*(X)\) for many spaces \(X\) without further reference to the actual definition of \(H^*(X)\). We will spend a large part of the course working through [ECS]. This describes the topological properties of a range of interesting spaces that occur naturally, and calculates their cohomology rings, some of which have a rich and interesting structure.

All the above files are in reasonably good shape, but nonetheless I may upload updated versions as the course progresses.

Interactive demonstrations

There is a set of interactive demonstrations explaining many of the ideas in the course. I will talk through some of these in lectures, there are attached YouTube videos, and you can try them yourself at other times. These are experimental and under development. I welcome comments about the extent to which they are comprehensible, useful or interesting.

These were originally prepared for a different course, so not all of them are directly relevant for MAGIC064.




The assessment for this course will be released on Monday 1st May 2023 and is due in by Friday 12 May 2023 at 23:59. Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period). You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period). If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Contact details

Neil Strickland
Hicks Building, Room J26
0114 2223852