mod-02-lec-09-a-first-classification-of-riemann-surfaces

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Interactive video lesson plan for: Mod-02 Lec-09 A First Classification of Riemann Surfaces

Activity overview:

An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves by Dr. T.E. Venkata Balaji, Department of Mathematics, IIT Madras. For more details on NPTEL visit http://www.nptel.iitm.ac.in/syllabus/111106044/

Goals of the Lecture:

- To get an idea of the classification of Riemann surfaces that can be arrived at
based on the fundamental group, using the theory of covering spaces

- To get introduced to the notions of : moduli problem, moduli space, number of
moduli, fine and coarse classification, and to write these down for simple Riemann
surfaces

Keywords:

Biholomorphic map or isomorphism of Riemann surfaces, classification of Riemann
surfaces, universal covering of a Riemann surface, abelian fundamental group,
complex plane, unit disc, upper half-plane, punctured plane, punctured unit disc,
cylinder, complex torus, annulus, Riemann sphere, g-torus, coarse classification,
fine classification, moduli problem, moduli theory, moduli space, number of moduli

Tagged under: A First Classification Riemann Surfaces

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