Open Gromov-Witten theory on Calabi-Yau three-folds I

Abstract

We propose a general theory of the Open Gromov-Witten invariant on Calabi-Yau three-folds. We introduce the moduli space of multi-curves and show how it leads to invariants. Our construction is based on an idea of Witten. In the special case that each connected component of the Lagrangian submanifold has the rational homology of a sphere we define rational numbers $F_{g,h}$ for each genus $g$ and $h$ boundary components.

arXiv commentImproved exposition

Cited by in corpus (2)

• Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces
• Open Mirror Symmetry for Higher Dimensional Calabi-Yau Hypersurfaces