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

TL;DR

This paper develops a comprehensive theory for Open Gromov-Witten invariants on Calabi-Yau three-folds, introducing a moduli space of multi-curves and defining rational invariants in specific cases, based on Witten's ideas.

Contribution

It introduces a new framework for Open Gromov-Witten invariants on Calabi-Yau three-folds using moduli spaces of multi-curves, extending previous approaches.

Findings

Defined the moduli space of multi-curves for Calabi-Yau three-folds.

Constructed invariants based on Witten's ideas.

Established rational numbers $F_{g,h}$ for certain Lagrangian submanifolds.

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.