Exotic G2-manifolds

Diarmuid Crowley, Johannes Nordström

Research output: Contribution to journalArticle

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.
Original languageEnglish
Number of pages28
JournalMathematische Annalen
Early online date8 Jun 2020
DOIs
Publication statusE-pub ahead of print - 8 Jun 2020

Keywords

  • math.AG
  • math.DG
  • math.GT
  • 14J28, 57R55 (Primary), 53C25 (Secondary)

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