Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Complete non-compact G2-manifolds from asymptotically conical Calabi-Yau 3-folds

Lorenzo Foscolo

created by risa on 11 May 2018

16 may 2018 -- 14:00

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


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.

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