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

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

250 students enrolled

Lecture 22: Torsion-freeness of the Fundamental Group of a Riemann Surface

Up Next
You can skip ad in
SKIP AD >
Advertisement
      • 2x
      • 1.5x
      • 1x
      • 0.5x
      • 0.25x
        EMBED LINK
        COPY
        DIRECT LINK
        PRIVATE CONTENT
        OK
        Enter password to view
        Please enter valid password!
        0:00
        0 (0 Ratings)

        Lecture Details

        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

        LECTURES



        Review


        0

        0 Rates
        1
        0%
        0
        2
        0%
        0
        3
        0%
        0
        4
        0%
        0
        5
        0%
        0

        Comments Added Successfully!
        Please Enter Comments
        Please Enter CAPTCHA
        Invalid CAPTCHA
        Please Login and Submit Your Comment

        LECTURES