Abstract
This paper is a review of current developments in the study of moduli spaces of G2manifolds. G2manifolds are seven-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be considered as an analogue of Calabi–Yau manifolds in seven dimensions. They play an important role in physics as natural candidates for supersymmetric vacuum solutions of M-theory compactifications. Despite the physical motivation, many of the results are of purely mathematical interest. Here we cover the basics of G2manifolds, local deformation theory of G2structures and the local geometry of the moduli spaces of G2structures.
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