Abstract/Details

## Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions

Solomon, Jake P.   Massachusetts Institute of Technology ProQuest Dissertations Publishing,  2006. 0809080.

### Abstract (summary)

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.)

### Indexing (details)

Subject
Mathematics;
Particle physics
Classification
0405: Mathematics
0798: Particle physics
Identifier / keyword
Pure sciences; Holomorphic curves; Intersection theory; Lagrangian boundary conditions; Moduli space
Title
Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
Author
Solomon, Jake P.
Number of pages
0
Degree date
2006
School code
0753
Source
DAI-B 67/06, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
Tian, Gang
University/institution
Massachusetts Institute of Technology
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
0809080
ProQuest document ID
304947035