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Sebastian Goette (Universität Freiburg): The Crowley-Nordström \nu-Invariant (20/05/2014)


Crowley and Nordström have found a Z/48-valued invariant \nu for topological G_2 structures on 7-compact manifolds.

Using an intrinsic description in terms of eta-invariants and Mathai-Quillen currents, we lift nu to an integer-valued invariant for G_2 holonomy metrics.

We compute this invariant for a certain range of examples and describe how it can distinguish different connected components of the space of G_2 holonomy metrics.

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