# Complete non-compact G2-manifolds from asymptotically conical Calabi-Yau 3-folds

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Lorenzo Foscolo

created by risa on 11 May 2018

16 may 2018
-- 14:00

Aula G, Dip.Matematica, Università "La Sapienza", Roma

**Abstract.**

G2-manifolds are the Riemannian 7-manifolds with G2 holonomy and in many
respects can be regarded as 7-dimensional analogues of Calabi-Yau 3-folds.
In joint work with Mark Haskins and Johannes Nordström we construct
infinitely many families of new complete non-compact G2 manifolds (only
four such manifolds were previously known). The underlying smooth
7-manifolds are all circle bundles over asymptotically conical Calabi-Yau
3-folds. The metrics are circle-invariant and have an asymptotic geometry
that is the 7-dimensional analogue of the geometry of 4-dimensional ALF
hyperkähler metrics. After describing the main features of our construction
I will concentrate on some illustrative examples, describing how recent
results in Calabi-Yau geometry about isolated singularities and their
resolutions can be used to produce examples of complete G2-manifolds.