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BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Cohomogeneity one manifolds with holonomy $G_2$ and Spin(7) Lehmann, Fabian


One of the most important ideas in the study of differential equations is the use of symmetries to cut down the number of variables. As manifolds with exceptional holonomy cannot be homogeneous the most symmetric case are group actions with cohomogeneity one, i.e. where a generic orbit has codimension one. In this case the PDE system is reduced to an ODE system. I will give an overview of recent progress in the construction of cohomogeneity one metrics with holonomy $G_2$ and Spin(7). All complete examples have a asymptotically locally conical (ALC) or asymptotically conical (AC) geometry at infinity.

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