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Authors: Farajzadeh Tehrani, Mohammad
Advisors: Tian, Gang
Contributors: Mathematics Department
Keywords: Gromov-Witten theory
Moduli space
Real curves
Symplectic cut
Symplectic geometry
Subjects: Mathematics
Issue Date: 2012
Publisher: Princeton, NJ : Princeton University
Abstract: Given a symplectic manifold $(X,\omega)$, an almost complex structure $J$, and an antisymplectic involution $\phi$, 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.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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