MA3H6 Algebraic topology
Term II 2013

Course 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 of a space, in some technical senses, is less powerful than its homotopy groups (the first of these is the fundamental group). However homology is far easier to compute and generalizes more directly to other areas of mathematics.

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


The schedule has a planned list of topics, organized by lecture. We will change the schedule as necessary, as we work through the material. Links to example sheets will be posted week-by-week.

Instructor and TA

Name Building/Office E-mail Phone Office Hours
Saul Schleimer 38/B2.14 s dot schleimer at warwick dot ac dot uk 024 7652 3560 Friday 3:10-4pm
Rupert Swarbrick 38/B2.34 r dot j dot swarbrick at warwick dot ac dot uk NA Tuesday and Thursday 2pm
Ian Vincent 38/B0.15 i dot vincent at warwick dot ac dot uk NA NA

Class meetings

Activity Led by Time Building/Room
Lecture Schleimer Monday 5-6pm 38/MS.05
Support class Swarbrick Tuesday 10-11am 38/A1.01
Lecture Schleimer Thursday 10-11am 38/MS.04
Support class Vincent Friday 12-1pm 38/B1.01
Lecture Schleimer Friday 2-3pm 38/MS.04

Reference materials

We will closely follow chapter two of the book Algebraic topology, by Allan 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.

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 course last term: revision on Abelian groups and exercise sheets one and two.


The exam will be 85% of your mark. The exam will be closed book. Prof. David Mond has kindly made the final exam from his course in 2012 available. If you find exams from earlier years, please send me a copy to post here.

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.

Homework solutions must be turned into Rupert Swarbrick at the beginning of the Tuesday support class or handed into his box in the supervisors' pigeon loft by 10am. No late work will be accepted. Please write your name, the date, and the problem you are solving at the top of the page. Solutions typeset using LaTeX are preferred. Please 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.


Please tell me in person, or via email, about any errors on this website or made in class. I am especially keen to hear about mathematical errors, gaffes, or typos made in lecture or in the example sheets.