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Title:
The extended v -invariant — progress and problems
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Abstract:
We recall the definition of the extended \nu-invariant, which distinguishes connected components of the moduli space of compact Riemannian manifolds whose holonomy group is G_2 (G_2-manifolds for short). All known computations of \nu(M,g) for G_2-manifolds (M,g) give values that are divisible by three. This implies that all these examples are topologically G_2-nullbordant. It is therefore interesting to know if 3|\nu(M,g) for all G_2-manifolds. We will report on results and projects related to this question.
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