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Title:
Fundamentals of exceptional holonomy, II
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Abstract:
This is part two of an introduction to the geometry of G_2 and spin-7 structures, henceforth called “exceptional structures”. We will begin with the complete non-compact examples of exceptional manifolds due to Bryant-Salamon and other cohomogeneity one examples. We will explain the relation of these examples to G_2 and spin-7 cones and discuss the Riemannian geometry of their links. We will briefly mention Joyce’s perturbative existence theorem of torsion-free exceptional structures given appropriate initial data used for compact constructions of smooth compact G_2 manifolds. This topic will be treated in great detail in the later lectures of Haskins and Nordstrom. Finally, we will establish the smoothness of the moduli space of compact G_2 manifolds and discuss some special geometric structures on this moduli space.
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