New complete metrics with holonomy G_2

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• Johannes Nordstrom, Bath
• Wednesday 20 February 2019, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

I will discuss new constructions of complete Riemannian 7-manifolds with holonomy G_2 from joint work with Lorenzo Foscolo and Mark Haskins (arXiv:1709.04904 and arXiv:1805.0261). From circle bundles over 3-dimensional Calabi-Yau cones we obtain infinitely many diffeomorphism types of complete G_2-manifolds with “asymptotically locally conical” ends, ie the end is approximately a circle bundle with fibres of constant circumference over a Calabi-Yau cone. In the special case of circle bundles over the Calabi metric on the total space of the canonical bundle of P1 x P1, these metrics have cohomogeneity one, making it possible to identify an asymptotically conical limit. This way we find also infinitely many topologically distinct examples of asymptotically conical G_2-manifolds.

This talk is part of the Differential Geometry and Topology Seminar series.

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