标题： 带有锥形奇点的紧致弱G_2流形 显示英文标题

标题： Compact weak G_2-manifolds with conical singularities

摘要： 我们构建了具有锥形奇点的7维紧致Einstein空间，这些空间保留了M理论中1/8的超对称性。 从数学上讲，它们具有弱G_2-全纯性。 我们证明，对于每一个渐近于6流形Y上的锥体的非紧致G_2-全纯流形，存在一个对应的具有两个锥形奇点的弱G_2流形，它在奇点附近看起来像一个Y上的锥体。 我们的构造提供了这些弱G_2流形上的显式度量。 我们完全根据Y的上同调确定了这些流形的上同调。 显示英文摘要

摘要： 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.