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

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

427 students enrolled

Lecture 28: Quotients by Kleinian Subgroups give rise to Riemann Surfaces

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 see how the quotient of the region of discontinuity by a Kleinian subgroup of Moebius transformations is a union of Riemann surfaces To see how the quotients above are ramified (or) branched coverings of Riemann surfaces, with ramifications at the points with nontrivial isotropies (stabilizers) To see in detail how to get a complex coordinate chart at the image point of a point of ramificationKeywords Upper half-plane, unimodular group, fixed point, projective special linear group, quotient by a subgroup of Moebius transformations, holomorphic automorphisms, extended plane, properly discontinuous action, stabilizer (or) isotropy subgroup, region of discontinuity of a subgroup of Moebius transformations, limit set of a subgroup of Moebius transformations, elliptic Moebius transformations, isolated point, discrete subset, Kleinian subgroup of Moebius transformations, quotient topology, ramification (or) branch points, ramified (or) branched covering, unramified (or) unbranched covering, branch cut, slit disc

        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