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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. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Details

Title
Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
Author
Solomon, Jake P.
Year
2006
Publisher
ProQuest Dissertations & Theses
Source type
Dissertation or Thesis
Language of publication
English
ProQuest document ID
304947035
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.