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/

Goal of Lecture 12:

To understand how the fundamental group based at a point of the target of a covering map acts naturally on the fiber of the covering map over that point, the fiber being thought of as embedded inside the source of the covering map.

Keywords for Lecture 12:

Path, lifting of a path, unique-path-lifting property, Covering Homotopy Theorem, surjective local homeomorphism, universal covering space, injective group homomorphism, fundamental group, simply connected space, trivial group, fiber of a covering map, coset space, group action, orbit, orbit map, stabilizer subgroup, fibration.