Exotic G_2-manifolds

  title={Exotic G_2-manifolds},
  author={D. Crowley and Johannes Nordstrom},
  journal={arXiv: Algebraic Geometry},
  • D. Crowley, Johannes Nordstrom
  • Published 2014
  • Mathematics
  • arXiv: Algebraic Geometry
  • 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. 
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