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 give a better definition of a Riemann surface using equivalence of atlases
– To define the notion of a holomorphic (or) analytic map from one Riemann surface
into another Riemann surface and in particular an isomorphism of Riemann surfaces
Keywords for Lecture 3:
Complex atlas, equivalent atlases, union of equivalent atlases, maximal atlas, holomorphic (or) analytic mapping between Riemann surfaces, isomorphism of Riemann surfaces