Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
"A new construction of compact $G_2$~manifolds by glueing Eguchi-Hanson spaces, Part II: Modifying the identification with the normal bundle"
This is the second in a series of talks, where I will go through the details of my new construction with Dominic Joyce of smooth compact $G_2$~manifolds by glueing families of Eguchi-Hanson spaces. In fact, this glueing involves three pieces, rather than two, and two of the three pieces \emph{do not} admit natural torsion-free $G_2$~structures, which makes the construction much more complicated than the only other existing constructions, by Joyce (1994) and by Kovalev/Corti-Haskins-Nordstr\"om-Pacini (2003/2012). In the second talk, I will discuss both 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. If time permits we will discuss the next major component of the construction, namely the fibre-wise blow up of the orbifold to obtain a family of topologically Eguchi-Hanson spaces.
MC 5479