Compact weak G_2-manifolds with conical singularities

Abstract

We construct 7-dimensional compact Einstein spaces with conical singularities that preserve 1/8 of the supersymmetries of M-theory. Mathematically they have weak G_2-holonomy. We show that for every non-compact G_2-holonomy manifold which is asymptotic to a cone on a 6-manifold Y, there is a corresponding weak G_2-manifold with two conical singularities which, close to the singularities, looks like a cone on Y. Our construction provides explicit metrics on these weak G_2-manifolds. We completely determine the cohomology of these manifolds in terms of the cohomology of Y.

26 pages, Latex, version to be published in Nucl. Phys. B, minor changes, one appendix added

References in corpus (1)

• Anomalies in M-theory on singular G_2-manifolds

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