Abstract:
We study 7-manifolds of holonomy SU(2) \rtimes F and partially classify them. Orbifold limits of such spaces have singular sets of the type considered by Joyce and Karigiannis who showed that (1707.09325), under certain conditions, such singular spaces can be desingularised to smooth, compact, G2-manifolds. We obtain a complete understanding of the physics of these spaces in the context of M-theory, although this will not feature much in the talk. As a bonus we discover an unexpected isomorphism between two seemingly unrelated moduli spaces: the space of Ricci flat metrics on these 7-manifolds and the space of flat connections on compact, flat 3-manifolds.