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Spiro Karigiannis: Lectures

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 G_2~manifolds (joint work with Dominic Joyce). We resolve (X^6 \times S^1)/\mathbb Z_2 by glueing in a family of Eguchi–Hanson spaces parametrized by the singular set, two copies of a special Lagrangian submanifold L^3 in X^6. 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 G_2~structures to start with, so we need to work harder to construct a closed G_2~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.