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arXiv · 1411.0656

Exotic G_2-manifolds

Diarmuid Crowley·Johannes Nordström
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Abstract

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.

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Diarmuid Crowley, Johannes Nordström. 2014-11-03. Exotic G_2-manifolds. https://arxiv.org/abs/1411.0656

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