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arXiv · hep-th/0302021

Compact weak G_2-manifolds with conical singularities

Adel Bilal·Steffen Metzger
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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.

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Adel Bilal, Steffen Metzger. 2003-04-25. Compact weak G_2-manifolds with conical singularities. https://doi.org/10.1016/s0550-3213(03)00388-2

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