Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01ht24wj46g
 Title: ON MODULI SPACES OF REAL CURVES IN SYMPLECTIC MANIFOLDS Authors: Farajzadeh Tehrani, Mohammad Advisors: Tian, Gang Contributors: Mathematics Department Keywords: Gromov-Witten theoryModuli spaceReal curvesSymplectic cutSymplectic 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. URI: http://arks.princeton.edu/ark:/88435/dsp01ht24wj46g 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