Welcome

This course unit will provide an introduction to the hyperbolic plane and hyperbolic geometry and study how discrete groups of isometries act on the hyperbolic plane.

If you have any questions please do not hesitate in contacting me:

Where to find course information

On the Course Information page you will find important information about this course including: course learning outcomes and details of the course syllabus. In addition you will want to read Succeeding in this Course Unit, also in the Course Information section.

Your course assessment information will appear on the Assessment & Feedback page where you will also find details here of what feedback you will receive during the course, when you will receive it and how it can help in your future assessment tasks.

Course materials and resources can be found below.

Lecture notes & Exercises and Solutions

The lectures notes for the course can be found here:

The lecture notes also contain the exercises and solutions to the exercises.

I will trust you to have a serious attempt at the exercises before referring to the solutions.

(If you're from outside Manchester and are looking for the previous version of these notes - which included material on limit sets of Fuchsian groups - then you can find them here.)

Hand-written slides from the lectures

Below are the visualiser slides from the lectures. My advice would be to read the printed lecture notes above rather than to read the slides; however they may be useful if you want to double-check what I wrote in a lecture.

Week 1, Week 2, Week 3, Week 4, Week 5, Week 7 (and clarification of the defintion of Dirichlet polygon) , Week 8, Week 9, Week 10, Week 11 (updated), Week 12 (revision lectures).

Additional resources

Some links that are discussed in the lectures (note: some are out-of-date):

Lecture podcasts can be accessed from https://video.manchester.ac.uk/lectures (requires sign in).