May 13, 2024
TITLE: On the Moduli Space of G2 Manifolds
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 a non-trivial element in the second homotopy group of the more accessible observer moduli space of G2 metrics on one of Joyce’s examples. If time permits, I will indicate why and how this non-trivial example might also descend to the (full) moduli space.
This talk is based on ongoing joint work with Sebastian Goette.
