# MAGIC064 Algebraic Topology Lecturer: Neil Strickland

## Module information

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

## Lectures

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:

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.

## Assessment

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
N.P.Strickland@sheffield.ac.uk
Hicks Building, Room J26
0114 2223852