Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
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71016011-MIT.pdf
Description
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Author(s)
Solomon, Jake P. (Jake Philip)
Advisor(s)
Gang Tian.
Date Issued
2006
Publisher
Massachusetts Institute of Technology
Abstract
We define a new family of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold arises as the fixed points of an anti-symplectic involution and has dimension 2 or 3. In the strongly semi-positive genus 0 case, the new invariants coincide with Welschinger's invariant counts of real pseudoholomorphic curves. Furthermore, we calculate the new invariant for the real quintic threefold in genus 0 and degree 1 to be 30. The techniques we introduce lay the groundwork for verifying predictions of mirror symmetry for the real quintic.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
Includes bibliographical references (p. 107-109).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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