Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
"A new construction of compact $G_2$ manifolds by glueing Eguchi-Hanson spaces, Part III.b: Fibrewise blow-up by a family of Eguchi-Hanson spaces, continued"
We continue with the second of four main steps of the construction: resolving the orbifold singularities by performing a fibre-wise blow up. The important point is that there is no natural torsion-free G2 structure on this third glueing region. The natural G2 structure is not even closed. There is a natural way to correct it to be closed, which we will discuss. The third step will then be to correct this further to remove the leading error term in the torsion, by solving an elliptic equation on each fibre.
MC 5479