G2 manifolds from nodal Calabi-Yau 3-folds

G2 manifolds from nodal Calabi-Yau 3-folds

-
Lorenzo Foscolo, University College London

Zoom linkhttps://princeton.zoom.us/j/594605776

I will discuss joint work with Mark Haskins and Johannes Nordström on the construction of families of 7-dimensional Ricci-flat manifolds with holonomy G2 close to a limiting Calabi-Yau 3-fold (modulo an antiholomorphic involution) with nodal singularities.  

In the first part of the talk I will describe the non-compact situation, where the limiting Calabi-Yau 3-fold is the conifold itself or its smoothing or small resolution. In this context, our results provide a precise metric realisation of work by Atiyah-Maldacena-Vafa and Acharya in the early 2000’s on large N-duality in Type IIA String theory and its lift to M-theory. 

In the second part of the talk, I will report on work in progress in the compact case, where the non-compact spaces above appear as building blocks in a gluing construction. I will explain the central role in the construction of a topological constraint analogous to Friedman’s necessary and sufficient condition for smoothing nodal Calabi-Yau 3-folds. I will also describe how the construction can be modified to obtain compact G2-spaces with isolated conical singularities.