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

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

Updated On 02 Feb, 19

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

Updated On 02 Feb, 19

- On-demand Videos
- Login & Track your progress
- Full Lifetime acesses

4.1 ( 11 )

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 To analyze what the conditions of loxodromicity, ellipticity or hyperbolicity imply for an automorphism of the upper half-plane, i.e., to characterize the automorphisms of the upper half-plane. This is required for the classification of Riemann surfaces with universal covering the upper half-plane To show that the fundamental group of a Riemann surface is torsion free i.e., that it has no non-identity elements of finite order To show that the Deck transformations of the universal covering of a Riemann surface have to be either hyperbolic or parabolic in nature To deduce that the fundamental group of a Riemann surface is torsion freeKeywords Moebius transformation, special linear group, projective special linear group, parabolic, elliptic, hyperbolic, loxodromic, fixed point, conjugation, translation, Riemann sphere, extended complex plane, upper half-plane, square of the trace (or trace square) of a Moebius transformation, torsion-free group, element of finite order of a group, torsion element of a group, universal covering, fundamental group, Deck transformations

Sam

Sep 12, 2018

Excellent course helped me understand topic that i couldn't while attendinfg my college.

Dembe

March 29, 2019

Great course. Thank you very much.