MA3H6 Algebraic topology
Term II 2016-2017
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 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:
- It is far easier to compute.
- 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.
The schedule has a planned list of
topics, organized by lecture. We will alter the schedule as the class
and the material require it. Links to example sheets will be posted
Instructor and TAs
||s dot schleimer at warwick dot ac dot uk
||024 7652 3560
||Tuesday, 15:00 - 16:00
||L dot Campo at warwick dot ac dot uk
|Esmee te Winkel
||E dot Te-Winkel at warwick dot ac dot uk
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
Another book on this topic, with a very different viewpoint, is Algebraic
topology, a first course by William Fulton.
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.
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.
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.
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