Type
Text
Type
Dissertation
Advisor
Bowman, Joshua | Takhtajan, Leon A | Bishop, Christopher | Velling, John A.
Date
2012-05-01
Keywords
Mathematics | Complex Analysis, Teichm??ller Theory
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71417
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
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). | 53 pages
Recommended Citation
Song, Ki Woo, "Teichm??ller Space of a Once Punctured Disk: Complex Coordinates on the Space of Abelian Differentials and the Takhtajan-Zograf Metric" (2012). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 623.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/623