# Infinitely many new families of complete cohomogeneity one G2-manifolds

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Lorenzo Foscolo

created by daniele on 02 May 2018

7 may 2018
-- 14:30

Aula Tricerri, DiMaI, Firenze

**Abstract.**

G2-manifolds are the 7-dimensional Riemannian manifolds with holonomy the exceptional compact Lie group G2. G2-manifolds are Ricci-flat and conversely most known constructions of Ricci-flat metrics involve some form of holonomy reduction. I will present joint work with Mark Haskins and Johannes NordstrÃ¶m on SU(2)xSU(2)-invariant G2-holonomy metrics. Because they are Ricci-flat, G2-manifolds can only admit continuous symmetries when they are non-compact or incomplete. We obtain many complete and incomplete G2-metrics with interesting prescribed asymptotic geometry and/or singular behaviour. More precisely, we obtain infinitely many 1-parameter families of complete G2-metrics with non-maximal volume growth and so-called ALC asymptotics, infinitely many asymptotically conical G2-metrics, and the first known example of a G2-metric that has an isolated conical singularity in the interior, but is otherwise complete. Our infinitely many asymptotically conical examples are particularly noteworthy since only the three classical Bryant-Salamon examples from 1989 were previously known.