2026-09-20T01:16:08Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/345512022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Gang Tian.
Solomon, Jake P. (Jake Philip)
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2006-11-07T12:54:46Z
2006-11-07T12:54:46Z
2006
2006
http://hdl.handle.net/1721.1/34551
71016011
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
Includes bibliographical references (p. 107-109).
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.
by Jake P. Solomon.
Ph.D.
109 p.
4324877 bytes
4330908 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
Thesis
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