MA4J2, Three-Manifolds
Winter 2012

Course Description

This class, an introduction to the geometry of three-dimensional manifolds, is a natural extension of MA243 (Geometry) and MA3F1 (Introduction to Topology); these are essentially prerequisites. The modules MA3H6 (Algebraic Topology) and MA455 (Manifolds) are also extremely useful.


The schedule has a planned list of topics, organized by lecture. Links to example sheets will be posted week-by-week.

Instructor and Marker

Name Building/Office E-mail Phone Office Hours
Saul Schleimer 39/B2.14 s dot schleimer at warwick dot ac dot uk 024 7652 3560 Tuesday 2-3pm
Robert Tang 39/B2.01 robert dot tang at warwick dot ac dot uk N/A N/A

Class meetings

Activity Led by Time Building/Room
Support class Tang Monday 10-11am 39/B3.01
Lecture Schleimer Tuesday 12-1pm 39/B3.03
Scribe meeting Schleimer Wednesday 12-12:30pm 39/B2.14
Lecture Schleimer Thursday 12-1pm 39/B3.03
Lecture Schleimer Friday 3-4pm 39/B3.03

Reference materials

We will closely follow the article The geometries of 3-manifolds, by Peter Scott. Another very useful reference is the website Geometry and the imagination, by Conway, Doyle, Gillman, and Thurston. A more advanced reference is the book Three-dimensional geometry and topology, by William Thurston.

Last year's course focused more on the topology and algebra of three-manifolds. Several students in that class (Winstel, Pressland, Kitson, and Scott) prepared notes, with many lovely figures. Two of the main references for that class were:
Three-dimensional manifolds (Chapters 1-2, 3, 4-5, 6-7, 8-12, Exercises 1 and 2), by Marc Lackenby and
Notes on basic 3-manifold topology, by Allen Hatcher.

Other useful references include:
3-manifolds, by John Hempel.
Knots and links, by Dale Rolfsen.
The theory of normal surfaces, by Cameron Gordon, typeset by Richard Kent.
Topology of 3-dimensional fibered spaces, by Herbert Seifert.

Example sheets

See the schedule for the example sheets.


The exam will be 85% of your mark. The exam will be closed book. The 2011 exam is available. Please be aware that the contents of this module are very different; this exam should not be considered a practice exam.

Assessed work

Assessed work will be 15% of your mark. 2% (at most) may be earned every week (starting the second week) you turn in a single worked exercise. Alternatively, you may scribe a lecture to earn that week's marks. (Apply early! At most one student per lecture! While supplies last!)

Callum Duffy has made his LaTex file available for scribes to use.

Homework solutions must be turned into Robert Tang at the beginning of the support class. No late work will be accepted. Please include 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 example sheets.