Exotic G_2-manifolds
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2014
- arXiv:
- arXiv:1411.0656
- Bibcode:
- 2014arXiv1411.0656C
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Differential Geometry;
- Mathematics - Geometric Topology;
- 14J28;
- 57R55 (Primary);
- 53C25 (Secondary)
- E-Print:
- v4: minor corrections