Exotic G_2manifolds
Abstract
We exhibit the first examples of closed 7dimensional Riemannian manifolds with holonomy G_2 that are homeomorphic but not diffeomorphic. These are also the first examples of closed Ricciflat manifolds that are homeomorphic but not diffeomorphic. The examples are generated by applying the twisted connected sum construction to Fano 3folds of Picard rank 1 and 2. The smooth structures are distinguished by the generalised EellsKuiper invariant introduced by the authors in arXiv:1406.2226.
 Publication:

arXiv eprints
 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)
 EPrint:
 v4: minor corrections