TCC Introduction to three-manifolds
Term II 2020-2021

Module Description

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 this TCC 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.


Name Building/Office E-mail Phone Virtual office Hours
Saul Schleimer B2.14 Zeeman s dot schleimer at warwick dot ac dot uk 024 7652 3560 Friday 12:30-13:30 on Teams and by appointment

Class meetings

Activity Led by Time "Location"
Lecture Schleimer Wednesday 11:00-13:00 Teams

Reference materials

For the latter portion of the module we will follow the notes on three-manifolds by Andrew Casson. Other useful references include notes by Cameron Gordon, Allen Hatcher, Marc Lackenby (scroll down to Michaelmas 1999), and Danny Calegari. Of course, there is also Thurston's book, in its various versions. I also highly recommend Gordon's historical overview of the subject.

I will post copies of the lectures in the class schedule as they become available.

Example sheets

See the schedule for the example sheets. Hatcher's notes and Thurston's book also contain many interesting exercises.

Assessed work

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 example sheets.