MAGIC064 Algebraic Topology
Lecturer: Neil Strickland
There is a page for this course
on the MAGIC website.
Lectures will happen on Tuesdays and Thursdays, from 14:05 to 14:55.
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.
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
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%.
Hicks Building, Room J26