An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves

IIT Madras Course , Prof. T.E. Venkata Balaji

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Lecture 14: The Construction of the Universal Covering Map

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        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 httpwww.nptel.iitm.ac.insyllabus111106044Goals of Lecture 14 In the previous lecture, the universal covering space was constructed for a given space as a Hausdorff topological space along with a natural map into the given space. In this lecture, we show that this natural map is a covering map It would follow that if the given space is locally arcwise connected and locally simply connected, then the same properties hold for the universal covering space as wellKeywords for Lecture 14 Path, Fixed-end-point (FEP) homotopy equivalence class, fundamental group, pathwise or arcwise connected, Hausdorff, locally simply connected, universal covering, basic open set, base for a topology, sub-base for a topology, admissible neighborhood

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