Exotic G2-manifolds

Diarmuid Crowley; Johannes Nordström

doi:10.1007/s00208-020-02009-1

Exotic G₂-manifolds

Diarmuid Crowley, Johannes Nordström

Department of Mathematical Sciences

Research output: Contribution to journal › Article

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 language	English
Number of pages	28
Journal	Mathematische Annalen
Early online date	8 Jun 2020
DOIs	https://doi.org/10.1007/s00208-020-02009-1
Publication status	E-pub ahead of print - 8 Jun 2020

Keywords

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

Access to Document

10.1007/s00208-020-02009-1Licence: CC BY

http://arxiv.org/abs/1411.0656

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Crowley, D., & Nordström, J. (2020). Exotic G₂-manifolds. Mathematische Annalen. https://doi.org/10.1007/s00208-020-02009-1

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