We exhibit the first examples of closed 7-dimensional Riemannian manifolds with holonomy G_2 that are homeomorphic but not diffeomorphic. These are also the first examples of closed Ricci-flat manifolds that are homeomorphic but not diffeomorphic. The examples are generated by applying the twisted connected sum construction to Fano 3-folds of Picard rank 1 and 2. The smooth structures are distinguished by the generalised Eells-Kuiper invariant introduced by the authors in arXiv:1406.2226.

中文翻译：

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异国情调的$$G_2$$-歧管

我们展示了同胚但非微分同胚的具有完整 G_2 的封闭 7 维黎曼流形的第一个例子。这些也是同胚但非微分同胚的封闭 Ricci-flat 流形的第一个例子。这些示例是通过将扭曲连接和构造应用于 Picard 等级 1 和 2 的 Fano 3 倍而生成的。平滑结构由作者在 arXiv:1406.2226 中引入的广义 Eells-Kuiper 不变量区分。