June 5, 2017
TITLE: Constructing compact G2 manifolds by resolving (Calabi-Yau 3-fold x S1)/Z2
ABSTRACT: I will give an overview of the proof of a new construction of compact ~manifolds (joint work with Dominic Joyce). We resolve ()/ by glueing in a family of Eguchi–Hanson spaces parametrized by the singular set, two copies of a special Lagrangian submanifold in . There are two key differences from the previous glueing constructions of Joyce and Kovalev/CHNP. First, there are three pieces being glued together rather than two, and second, two of the three pieces do *not* admit torsion-free ~structures to start with, so we need to work harder to construct a closed ~structure with sufficiently small torsion on the resolved space in order to apply Joyce’s fundamental existence theorem. Given the audience of experts, I plan to explain all of the main ideas and to give some of the details of each of the principal steps in the proof.