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    Teichm??ller Space of a Once Punctured Disk: Complex Coordinates on the Space of Abelian Differentials and the Takhtajan-Zograf Metric

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    Song_grad.sunysb_0771E_10914.pdf (432.2Kb)
    Date
    1-May-12
    Author
    Song, Ki Woo
    Publisher
    The Graduate School, Stony Brook University: Stony Brook, NY.
    Metadata
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    Abstract
    We construct an embedding of T(Z), the Teichm??ller space of Z--a Fuchsian group with a single parabolic generator--into the space of abelian differentials on the Riemann surface M = Z \ H. This "pre-Bers embedding" is much simpler, yet it still draws many parallels with the Bers embedding, such as the existence of a linear local right inverse. This gives rise to new complex coordinates which are compatible with the Bers coordinates. The differentials of the pre-Bers and the Bers embedding belong to a one parameter family of operators on the space of Beltrami differentials on M, which behaving nicely with the Takhtajan-Zograf metric on T(Z).
    Description
    53 pg.
    URI
    http://hdl.handle.net/1951/59868
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    • Stony Brook Theses & Dissertations [SBU] [1955]

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