Off-campus SJSU users: To download campus access theses, please use the following link to log into our proxy server with your SJSU library user name and PIN.
Publication Date
Summer 2017
Degree Type
Thesis - Campus Access Only
Degree Name
Master of Science (MS)
Department
Mathematics
Advisor
Slobodan Simić
Subject Areas
Mathematics
Abstract
We explore the geometric properties of Möbius transformations as mappings of the extended complex plane and use this viewpoint to introduce the idea of a Riemann surface. We begin by discussing the key properties of Möbius transformations and emphasize the geometric viewpoint. In many places, we will avoid standard analytical proofs in a favor of geometric and constructive proofs. Then, we provide an introduction to the concept of a Riemann surface and show how subgroups of the general group of Möbius transformations generate Riemann surfaces via quotient spaces. The final goal is to explain the idea of the Uniformization Theorem and provide examples of various Riemann surfaces including compact surfaces of genus one.
Recommended Citation
Goulette, David Peter, "The Geometry of Möbius Transformations and an Introduction to Riemann Surfaces" (2017). Master's Theses. 4847.
DOI: https://doi.org/10.31979/etd.sv46-6y8e
https://scholarworks.sjsu.edu/etd_theses/4847
