TCC Introduction to three-manifolds
Term II 2020-2021
This module is intended as an introduction to three-manifolds, with
a particular focus on the sphere, disk, torus, and annulus theorems.
These are proved in various fashion, many times, in the literature.
We will follow notes of Casson and use the techniques of "PL-minimal
surface theory". These have the advantage of accessibility; they
also serve as an introduction to the "cut-and-paste" techniques
important for other structure theorems in the subject.
The prerequisites for
module are a good grasp of the fundamental group, of covering
spaces, and of simplical homology. A basic understanding of
manifolds and normal bundles will be helpful but I will attempt to
explain the required notions. The examples we will discuss, early
in the module, will require knowing a bit of spherical, euclidean,
and hyperbolic geometry. However, these are not essential.
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.
||Virtual office Hours
||s dot schleimer at warwick dot ac dot uk
||024 7652 3560
and by appointment
For the latter portion of the module we will follow the notes on
Casson. Other useful references include notes
Lackenby (scroll down to Michaelmas 1999),
Calegari. Of course, there is also Thurston's book, in
I also highly recommend Gordon's historical
of the subject.
I will post copies of the lectures in the
class schedule as they become
See the schedule for the example
sheets. Hatcher's notes and Thurston's book also contain many
There is no exam for this module. If you are taking the module for
credit you must complete one exercise every two weeks (for a total
of four) from the posted example sheets. These are to be written in
LaTex and sent to me for marking. The assignments are due on
Wednesday at 11:00 in the fourth, sixth, eighth, and tenth weeks of
Warwick term. (That is, just before the third, fifth, seventh, and
ninth (???) lectures.)
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