MA3H6 Algebraic topology
Term II 2013
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. 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
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 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 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