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 › peer-review

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 a previous paper.

Original language	English
Pages (from-to)	29–74
Number of pages	46
Journal	Mathematische Annalen
Volume	381
Issue number	1-2
Early online date	8 Jun 2020
DOIs	https://doi.org/10.1007/s00208-020-02009-1
Publication status	Published - 1 Oct 2021

ASJC Scopus subject areas

Mathematics(all)

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

Cite this

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AB - 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 a previous paper.

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Exotic G₂-manifolds

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Johannes Nordstrom

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Exotic G2-manifolds

Abstract

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Johannes Nordstrom

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Exotic G₂-manifolds