# 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.

## Problems

## 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 hoursâ€™ 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