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 a previous paper.
Original language | English |
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Number of pages | 28 |
Journal | Mathematische Annalen |
Early online date | 8 Jun 2020 |
DOIs | |
Publication status | E-pub ahead of print - 8 Jun 2020 |
ASJC Scopus subject areas
- Mathematics(all)