Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
"A new construction of compact G2~manifolds by glueing Eguchi-Hanson spaces, Part I: Overview"
This will be the first in a series of talks, where I will go through the details of my new construction with Dominic Joyce of smooth compact G2~manifolds by glueing families of Eguchi-Hanson spaces. In fact, this glueing involves three pieces, rather than two, and two of the three pieces do not admit natural torsion-free G2~structures, which makes the construction much more complicated than the only other existing constructions, by Joyce (1994) and by Kovalev/Corti-Haskins-Nordström-Pacini (2003/2012). In the first talk, I will begin with an outline of the basic strategy and ideas of the proof. Time permitting, we will then move on to the first of four major technical components of the proof: modifying the connection on the normal bundle and the exponential map in order to kill the leading errors in the torsion on the middle glueing piece.
MC 5403