Exotic G_2-manifolds
Algebraic Geometry
2020-05-11 v4 Differential Geometry
Geometric Topology
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.
Cite
@article{arxiv.1411.0656,
title = {Exotic G_2-manifolds},
author = {Diarmuid Crowley and Johannes Nordström},
journal= {arXiv preprint arXiv:1411.0656},
year = {2020}
}
Comments
v4: minor corrections; 28 pages; to appear in Math. Ann