DSpace Repository

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

Show simple item record

dc.contributor.advisor Takhtajan, Leon A en_US
dc.contributor.author Song, Ki Woo en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2013-05-22T17:35:36Z
dc.date.accessioned 2015-04-24T14:47:28Z
dc.date.available 2013-05-22T17:35:36Z
dc.date.available 2015-04-24T14:47:28Z
dc.date.issued 2012-05-01
dc.identifier Song_grad.sunysb_0771E_10914 en_US
dc.identifier.uri http://hdl.handle.net/1951/59868 en_US
dc.identifier.uri http://hdl.handle.net/11401/71417 en_US
dc.description 53 pgs en_US
dc.description.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). en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.subject.other Complex Analysis, Teichm??ller Theory en_US
dc.title Teichm??ller Space of a Once Punctured Disk: Complex Coordinates on the Space of Abelian Differentials and the Takhtajan-Zograf Metric en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Bowman, Joshua en_US
dc.contributor.committeemember Bishop, Christopher en_US
dc.contributor.committeemember Velling, John A en_US


Files in this item

This item appears in the following Collection(s)

Show simple item record

Search DSpace


Advanced Search

Browse

My Account