Differential Geometry Seminar: G2 Moduli Spaces May Have Holes

Speaker: Thorsten Hertl (University of Melbourne)

Title: G2 Moduli Spaces May Have Holes

Date: Friday 2 May 2025, 12:10pm in Napier 108

Abstract: In his two seminal articles, Dominic Joyce not only constructed the first examples of closed manifolds with G2-holonomy metrics, but also proved that the moduli space of all G2-metrics on a closed manifold is itself a finite-dimensional manifold. The statement is, however, only a local one, and the global topological properties of these moduli spaces have remained quite mysterious ever since. Indeed, up to now, we only know that they may be disconnected by the work of Crowley, Goette, and Nordström; the question whether all path components are contractible or not has not been answered yet.

In this talk, I will outline a construction of an element in the second homotopy group of the moduli space of G2 metrics on Joyce’s first example and present along the way a homotopy-theoretical result that guarantees its non-triviality.  This talk is based on joint work with Diarmuid Crowley and Sebastian Goette.