Abstracts of the Arbeitsgruppenseminar
Prof. Bernd Ammann und Mitarbeiter, Zimmer 119
Thorsten Hertl, The University of Melbourne
G2 Moduli Spaces May Have Holes
July 7th, 2025, 14:15
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 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.
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Bernd Ammann, 04.07.2025
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