MA3H6 Algebraic topology
Term II 2013-2014
This module, MA3H6
(Algebraic topology), is a continuation of, and has as its only
(Introduction to topology). Here we will begin the study of homology:
a collection of algebraic invariants of topological spaces. Though
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 technical
sense, record a simpler kind of information, homology scores over
homotopy in two important respects:
- It is far easier to compute.
- It generalizes more directly 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.
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 TAs
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
Another book on this topic, with a very different viewpoint, is Algebraic
topology, a first course by William Fulton.
See the schedule for the example
In addition to the exercise prepared for this class, please note that
Hatcher's book contains many interesting exercises. He has also given
exercises. Here are the exercises from Prof. Mond's module in 2012:
revision on Abelian groups and exercise
sheets one and two.
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 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.
Homework solutions must be turned in to Ian Vincent, or placed in his
supervisor's pigeonhole, by 12noon on Mondays. 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 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