This is the home page of MA40040: *Algebraic Topology* taught by Fran Burstall.

I keep a diary of what I covered in lectures. There is also an official syllabus and a reading list.

Here is the timetable. The problem class is on Mondays at 15:15.

Official office hours are on Thursdays 16:15-17:05. That
said, *any* hour that you can find me is an office
hour. Drop me an email if you want to guarantee a time that
I will be available.

Exercise sheets are issued weekly at the problem class and discussed at the next problem class after which solutions will appear here.

I will mark whatever you hand in, no matter when you hand it in, and normally get your work back to you within a week.

- Exercise sheet 1 with solutions as
`PDF`

. - Exercise sheet 2 with solutions as
`PDF`

. - Exercise sheet 3 with solutions as
`PDF`

. - Exercise sheet 4 with solutions as
`PDF`

. - Exercise sheet 5 with solutions as
`PDF`

. - Exercise sheet 6 with solutions as
`PDF`

. - Exercise sheet 7 as
`PDF`

.

This unit is assessed 100% by exam. Generic exam feedback and opportunities for individual exam feedback will be available early in semester 2.

By public demand and with some misgivings, I am making my lecture notes available in pdf format from the start of the course.

- The whole course, last updated: 11:32, Wednesday, October 24 2018.
- Unit outline: all the definitions and theorems, auto-generated from the course notes.

**WARNING**: these are not a substitute for taking your
own careful notes during lectures.

Look here for recordings of lecture, week 3 onwards (with sound from week 5).

Some articles or other resources that have some vague relevance to the course. For cultural interest only!

- A. Weinstein,
*Groupoids: Unifying Internal and External Symmetry*, Notices Amer. Math. Soc.**43**(1996) 744–752.The based homotopy classes of paths in a topological space form a groupoid rather than a group: read this to see other situations in which groupoids arise.

The Catsters: nearly eighty 10 minute videos on YouTube each explaining an aspect of Category Theory. Utterly fabulous!

David Calderbank has compiled a play-list.

*Basic Category Theory*is an excellent new introduction to category theory by Tom Leinster who has made it freely available on-line.

Here are potted biographies of some of the heroes that built Algebraic Topology:

- Henri PoincarĂ© 1854–1912
- The last of the great universal mathematicians and the inventor of the fundamental group.
- LEJ Brouwer 1881–1966
- He of Brouwer Fixed Point Theorem fame.
- K Borsuk 1905–1982
- Co-discoverer of the Borsuk-Ulam theorem and the inventor of retracts.
- Stan Ulam 1909–1984
- Co-discoverer of the Borsuk-Ulam theorem, inventor of Monte-Carlo method in statistical sampling and the guy who worked out how to make hydrogen bombs work!

There are many more biographies at the St Andrews history site.

I welcome feedback in the form of
*constructive* comments or criticism.

If you encounter any problems while using this site, send me mail describing as completely as you can what has gone wrong.

Fran Burstall
<feb@maths.bath.ac.uk>
Last modified: Wed Oct 24 16:13:46 BST 2018