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

### Revision activity

If you want a revision lecture, organise among yourselves to identify a time and topics. Then let me know!

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 1515.

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 with solutions as
`PDF`

. - Exercise sheet 8 with solutions 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.

Here are some past examination papers. Solutions are available online and in the Academic Reserve Collection of the Library.

- The 2017 exam as
`PDF`

. - The 2016 exam as
`PDF`

. - The 2015 exam as
`PDF`

. - The 2014 exam as
`PDF`

. - The 2013 exam as
`PDF`

.

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: 20:02, Saturday, January 13 2018.
- Unit outline: all the definitions and theorems, auto-generated from the course notes.
- Category theory and higher homotopy groups: Barnaby Sherratt's notes from the extra lectures. Thanks, Barnaby, for typing these up and making them available!

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

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: Sat Jan 13 20:02:38 GMT 2018