MA3H6 Algebraic topology
Term II 2016-2017

Module Description

This module, MA3H6 (Algebraic topology), is a continuation of, and has as its only prerequisite, MA3F1 (Introduction to topology). Here we will begin the study of homology: a collection of algebraic invariants of topological spaces. The homology groups \(H_k(X)\) of a space \(X\) are more difficult to define than the homotopy groups \(\pi_k(X)\) and, in some sense, record a simpler kind of information. However, homology scores over homotopy in two important respects:

1. It is far easier to compute.
2. It generalizes easily to other areas of mathematics.

The material covered in this module is directly relevant to MA3H5 (Manifolds) and MA4J7 (Cohomology and Poincaré duality), as well as to MA4A5 (Algebraic geometry) and many others.

Schedule

Instructor and TAs

Class meetings

Reference materials

We will closely follow chapter two of the book Algebraic topology, by Allen Hatcher. The book is available from the website above, and can also be purchased from the university bookshop or on-line.

Another book on this topic, with a very different viewpoint, is Algebraic topology, a first course by William Fulton.

Lecture capture is recording all lectures (audio only).

There is a forum for the module. Any questions sent to me via email will be answered there. I have also asked the TAs to keep an eye the forum.

Example sheets

See the schedule for the example sheets.

In addition to the exercise prepared for this class, please note that Hatcher's book contains many interesting exercises. He has also given additional exercises. Here are the exercises from Prof. Mond's module in 2012: revision on Abelian groups and exercise sheets one and two.

Exam

The exam will be 85% of your mark. The exam will be closed book. Here are the exam papers for this module from the last five years.

Assessed work

Assessed work will be 15% of your mark. Of this, 2% (at most) may be earned every week (starting the second week) by turning in a single worked exercise. Please let me (Saul) know if any of the problems are unclear or have typos.

Work is due Wednesdays at 14:00 in front of the undergraduate office. No late work will be accepted. Please write your name, the date, and the problem you are solving at the top of the page. If you collaborate with other students, please include their names. Solutions typeset using LaTeX are preferred. Please try to limit your solution to one piece of paper -- if more space is needed then write out a complete solution and then rewrite with conciseness in mind.

Mistakes