Date: Friday, December 01, 2017
Location: 3866 East Hall (3:00 PM to 4:00 PM)
Title: G2structures and octonion bundles
Abstract: We use a G2structure on a 7dimensional Riemannian manifold to define an octonion bundle with a fiberwise nonassociative product. We then define a metriccompatible octonionic covariant derivative on this bundle that is also compatible with the octonion product. The torsion of the G2structure is then shown to be an octonionic connection for this covariant derivative with curvature given by the component of the Riemann curvature that lies in the 7dimensional representation of G2. The choice of a particular G2structure within the same metric class is then interpreted as a choice of gauge and we show that under a change of this gauge, the torsion transforms as an octonionvalued connection 1form. We then also define an energy functional for octonion sections, the critical points of which are shown to correspond to an octonionic analog of the Coulomb gauge. The gradient flow for this functional is an octonionic harmonic map heat flow that minimizes the torsion within the same metric class.
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Speaker: Sergey Grigorian
Institution: UTRGV
Event Organizer: Dan Burns
