The moduli space of Ricci-flat metrics

Klaus Kr\"oncke (Hamburg)

Abstract: We study the set of Ricci-flat Riemannian metrics on a given compact manifold M. 
We say that a Ricci-flat metric on M is structured if its pullback to the universal cover admits a parallel spinor.  
We show that the moduli space of structured Ricci-flat metrics is a finite-dimensional smooth manifold. 
The space of structured Ricci-flat metrics is an open and closed subset in the space of all Ricci-flat metrics. 
The holonomy group is constant along connected components and the dimension
of the space of parallel spinors as well. 

These results build on previous work by Nordstr\"om, Goto, Koiso, Tian & Todorov, Joyce, McKenzie, Wang and many others.
The important step is to pass from irreducible to reducible holonomy groups.

This is joint work with Bernd Ammann, Hartmut Wei{\ss} and Frederik Witt.