MA40040: Algebraic Topology

Welcome

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

The story so far

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

Exercise sheets

• 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.

Past exam papers

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

• The 2011 exam as PDF.
• The 2010 exam as PDF.
• The 2009 exam as PDF.
• The 2008 exam as PDF.
• The 2007 exam as PDF.

Lecture notes

By public demand and with some misgivings, I am making my lecture notes available in pdf format. This will happen chapter-by-chapter sometime after the lectures have taken place.

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

• Chapter 0: Topology: concepts and examples.
• Chapter 1: There is no chapter 1.
• Chapter 2: Homotopy and the fundamental group.
• Chapter 3: Covering spaces.

Extra Reading

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.

Hall of Fame

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

Henri Poincaré 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.

Feedback

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

Problems with this site?

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