TCC Introduction to three-manifolds
Term II 2017-2018

Module Description

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.

Schedule

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.

Instructor

Name Building/Office E-mail Phone Office Hours
Saul Schleimer B2.14 Zeeman s dot schleimer at warwick dot ac dot uk 024 7652 3560 Friday 14:00-15:00

Class meetings

Activity Led by Time Building/Room
Lecture Schleimer Wednesday 10:00-12:00 B0.06 Zeeman

Reference materials

There is no one reference for the module. Useful references include Hatcher's notes, Lackenby's notes (scroll down), Calegari's notes, and Thurston's book, in its various versions.

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

There is also a Google groups discussion 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.

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 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 module.

Mistakes

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.