Geometric Analysis Seminar

Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo

"A new construction of compact $G_2$ manifolds by glueing Eguchi-Hanson spaces, Part III.c: Constructing the closed pair on the Eguchi-Hanson bundle"

We conclude the second of main step of the construction: constructing a pair of positive 3 and 4 closed forms $(\varphi, \psi)$ such that $\Theta(\varphi) - \psi$, a measure of the torsion, is still not small enough to apply Joyce's existence theorem. We will then discuss the idea behind correcting this further to kill off the leading error term in the torsion.

MC 5479