Topological Quantum Field Theory for Calabi-Yau threefolds and G_2   manifolds
  We introduce a homology theory whose Euler characteristics counts ASD bundles over four dimensional co-associative submanifolds in (almost) G_2 manifolds.   As a TQFT, in relative situations, we have the Fukaya-Floer category of Lagrangians intersection in the moduli space of special Lagrangian submanifolds in CY threefolds. 
Naichung Conan Leung