# Tag Archives: Fundamental Domain

## Homework Assignment 3

Recall that the upper half plane consists of complex numbers with . Let denote the closed unit disk as the union of the unit disk with its boundary . This assignment is meant to explain the pictures at the Wolfram … Continue reading

## Lecture 13: Wednesday, September 18, 2013

In Lecture 11 and Lecture 12, we discussed examples of Riemann Surfaces and their relation with the Riemann Sphere . Today, we put things into perspective by considering the larger picture: we discuss tesselations of the upper half plane, covering … Continue reading

## Lecture 12: Monday, September 16, 2013

Last time, we introduced the Fundamental Domain in terms of the extended complex plane . Felix Klein showed the existence of a function , invariant under , giving these isomorphisms. Today, we use Richard Dedekind‘s function to create similar functions … Continue reading

## Lecture 11: Friday, September 13, 2013

Over the past several lectures, we have focused on triangle groups and ways to tesselate both the plane and the sphere. In order to generalize this, we will focus on ways to tesselate compact, connected Riemann surfaces. Today we’ll begin … Continue reading