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Title:
Disconnecting the G_2 moduli space
Speaker:
Abstract:
I will describe how the homotopy invariant of G_2-structures on closed 7-manifolds introduced in Diarmuid Crowley's talk can be defined analytically. This intrinsic definition makes it possible to compute the invariant for a class of closed G_2-manifolds generalising the well-known twisted connected sums, leading to examples of closed 7-manifolds where one can use the homotopy theory of G_2-structures to distinguish between connected components of the moduli space of holonomy G_2 metrics. Moreover, the analytic definition leads to a more refined invariant that can in some cases even distinguish between G_2-metrics whose associated G_2-structures are homotopic. This talk is based on joint work with Diarmuid Crowley and Sebastian Goette.
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