Disconnecting the G_2 Moduli Space

Author: 
Johannes Nordstrom
Date: 
Tue, Jul 7, 2015
Location: 
PIMS, University of British Columbia
Conference: 
PIMS Symposium on the Geometry and Topology of Manifolds
Abstract: 

Little is currently known about the global properties of the $ G_2 $ moduli space of a closed 7-manifold, ie the space of Riemannian metrics with holonomy $ G_2 $ modulo diffeomorphisms. A holonomy $ G_2 $ metric has an associated $ G_2 $-structure, and I will define a Z/48 valued homotopy invariant of a $ G_2 $-structure in terms of the signature and Euler characteristic of a Spin(7)-coboundary. I will describe examples of manifolds with holonomy $ G_2 $ metrics where the invariant is amenable to computation in terms of eta invariants, and which are candidates for having a disconnected moduli space. This is joint work in progress with Diarmuid Crowley and Sebastian Goette.

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