On contact homology of the unit cotangent bundle of a Riemann surface with genus greater than one

In this thesis, I study pseudo-holomorphic curves in symplectisation of the unit cotangent bundle of a Riemann surface of genus greater than 1. The contact form and compatible almost complex structure are both constructed from a metric on the Riemann surface whose curvature is constant -1. I related the pseudo-holomorphic curve equation to harmonic map equations and a Cauchy-Riemann type equation perturbed with quadratic terms for functions on a punctured Riemann sphere. Then I prove a Theorem that gives one to one correspondence between solutions to the perturbed Cauchy-Riemann equation and finite energy pseudo-holomorphic curves.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2003

Author dc:creator

• Luo, Wei, 1975-

Advisor dc:contributor.advisor

• Shing-Tung Yau.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/29984

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/29984