2014/11/03 by Crowley, Diarmuid, Nordström, Johannes
#14J28 #53C25 (Secondary) #57R55 (Primary) #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1411.0656
We exhibit the first examples of closed 7-dimensional Riemannian manifolds with holonomy G2 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.