Global structure of G2-moduli spaces

Characterize the global structure of the moduli space M of torsion-free G2-structures on a compact oriented 7-manifold M, beyond the established local descriptions.

Background

Joyce proved that the moduli space of torsion-free G2-structures on a compact 7-manifold is a smooth affine manifold of dimension b^3(M), with local models in cohomology. However, these results are local in nature and do not determine global geometric properties of the moduli space.

The paper emphasizes that the absence of an analogue of Yau's theorem in G2-geometry hinders global understanding. The authors introduce a new period-type immersion into a homogeneous space as a perspective, but the comprehensive global description of the moduli space remains unresolved.