  This article studies the geometry of moduli spaces of G2-manifolds,
associative cycles, coassociative cycles and deformed Donaldson-Thomas bundles.
We introduce natural symmetric cubic tensors and differential forms on these
moduli spaces. They correspond to Yukawa couplings and correlation functions in
M-theory.
  We expect that the Yukawa coupling characterizes (co-)associative fibrations
on these manifolds. We discuss the Fourier transformation along such fibrations
and the analog of the Strominger-Yau-Zaslow mirror conjecture for G2-manifolds.
  We also discuss similar structures and transformations for Spin(7)-manifolds.
