Title:Fundamentals of exceptional holonomy, II
Speaker: Spiro Karigiannis
Date: Wednesday, August 20, 2014
Time: 11:00am-12:00pm
Place: Seminar Room 313, Simons Center
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Abstract: This is part two of an introduction to the geometry of $\mathrm{G}_2$ and $\mathrm{Spin}(7)$ 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 $\mathrm{G}_2$ and $\mathrm{Spin}(7)$~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 $\mathrm{G}_2$~manifolds. This topic will be treated in great detail in the later lectures of Haskins and Nordstr\”om. Finally, we will establish the smoothness of the moduli space of compact $\mathrm{G}_2$~manifolds and discuss some special geometric structures on this moduli space.