TCC Introduction to three-manifolds
Term II 2017-2018
We will take a stroll through the field of three-manifolds, heading
in the general direction of the distant peaks of the homeomorphism
problem and the geometrisation theorem. More concretely: we will
begin the module with a focus on classic combinatoral topology of
three-manifolds in order to understand the hypotheses of the
geometrization theorem. We will then switch to a discussion of the
eight Thurston geometries in order to understand the conclusion of
the geometrisation theorem. If time permits, we will end with an
overview of the proof of geometrisation, and its application to the
homeomorphism problem. Throughout the module we place an emphasis
on the many beautiful examples that the subject offers.
The prerequisites for
this TCC module
are a good grasp of the fundamental group, covering spaces,
simplical homology, a basic understanding of manifolds, and a basic
understanding of spherical, euclidean, and hyperbolic geometry.
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.
||s dot schleimer at warwick dot ac dot uk
||024 7652 3560
Useful references include the notes on three-manifolds by
Lackenby (scroll down to Michaelmas 1999), and Danny
Calegari. Of course, there is also Thurston's book, in
I will post copies of the lectures in the
class schedule as they become
There is also a Google
forum where you can ask questions of myself and the class.
Please inform me if you or somebody you know would like to be added
as a participant.
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 write a five page "book report" (in LaTex, with a
reasonable layout) on one of the papers mentioned during the course.
This is due at 12:00 on 2018-05-04. We (that is, you and I) must
agree on the paper to be read by (or before) the final lecture of the
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