Intersection theory of coassociative submanifolds in G_(2)-manifolds and   Seiberg-Witten invariants
  We study the problem of counting instantons with coassociative boundary condition in (almost) G_(2)-manifolds. This is analog to the open Gromov-Witten theory for counting holomorphic curves with Lagrangian boundary condition in Calabi-Yau manifolds. We explain its relationship with the Seiberg-Witten invariants for coassociative submanifolds. 
Naichung Conan Leung and Xiaowei Wang