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On moduli spaces of real curves in symplectic manifolds.

Author: Mohammad Farajzadeh Tehrani; Princeton University. Department of Mathematics.
Dissertation: Thesis (Ph.D.)--Princeton University, 2012.
Edition/Format:   Thesis/dissertation : Thesis/dissertation : Manuscript : eBook   Archival Material : English
Publication:Dissertation Abstracts International, 74-04B.
Database:WorldCat
Summary:
Given a symplectic manifold (X, o), an almost complex structure J, and an antisymplectic involution &phis;, we study genus zero real J-holomorphic curves in X. There are two types of such curves, those that can be divided into two J-holomorphic discs and those that cannot. Moduli spaces of J-holomorphic discs are more studied in the literature; in this case, we develop and use some degeneration techniques to add to  Read more...
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Details

Material Type: Thesis/dissertation, Manuscript, Internet resource
Document Type: Internet Resource, Archival Material
All Authors / Contributors: Mohammad Farajzadeh Tehrani; Princeton University. Department of Mathematics.
ISBN: 9781267783875 1267783877
OCLC Number: 830511411
Notes: Source: Dissertation Abstracts International, Volume: 74-04, Section: B.
Tian, Gang, advisor.
Gunning, Robert C., committee member.
Sarnak, Peter, committee member.
Description: 57 p.

Abstract:

Given a symplectic manifold (X, o), an almost complex structure J, and an antisymplectic involution &phis;, we study genus zero real J-holomorphic curves in X. There are two types of such curves, those that can be divided into two J-holomorphic discs and those that cannot. Moduli spaces of J-holomorphic discs are more studied in the literature; in this case, we develop and use some degeneration techniques to add to the previous results and get a better understanding of these moduli spaces. We also study the second case, for which the orientation problem is different and define (and calculate) some invariants using these moduli spaces. As shown in this thesis, these two cases are tied together and often need to be combined to get a fully well-defined theory.

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