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Title:
ALC manifolds with special holonomy
Speaker:
Abstract:
At the meeting in January, I described a new analytic construction, obtained in joint work with Mark Haskins and Johannes Nordström, of complete non-compact G_2-manifolds. The construction starts with an asymptotically conical (AC) Calabi-Yau 3-fold B and produces a 1-parameter family of complete G_2-metrics on a suitable circle bundle over B. These G_2-metrics have asymptotically locally conical (ALC) geometry, the natural generalisation of the asymptotic geometry of ALF hyperkähler 4-manifolds to higher dimensions. In this talk I will describe some initial steps in two different directions related to that result. Firstly, I will show how in our construction of ALC G_2-manifolds rigid compact holomorphic curves in the AC Calabi-Yau 3-fold lift to rigid associative submanifolds in the ALC G_2-manifold. Secondly, I will describe the analogous construction of ALC Spin(7)-holonomy metrics on suitable circle bundles over AC G_2-manifolds.
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