Classifying Riemann surfaces
Wednesday, October 21st, 2009 | Author: Konrad Voelkel
In this post, I will sketch a classification of Riemann surfaces.
For those who haven't heard about the subject before, there is an introduction. For the impatient, look at the bottom of the post, where I have written a very short summary.
Table of contents:
- Examples and counter-examples
- Topological classification, the genus
- Digression about algebraic field extensions
- Biholomorphic classification via universal covering deck transformations
- Brief discussion of Gaussian curvature and conformal geometry
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