On contact homology of the unit cotangent bundle of a Riemann surface with genus greater than one
Name
54790531-MIT.pdf
Description
Full printable version
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2.46 MB
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5b67ffbc6265b9f0bc6faf51bfff9937
Author(s)
Luo, Wei, 1975-
Advisor(s)
Shing-Tung Yau.
Date Issued
2003
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.
Includes bibliographical references (p. 80).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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