### Abstract

Original language | English |
---|---|

Number of pages | 56 |

Journal | Proceedings of the London Mathematical Society |

Early online date | 26 Dec 2018 |

DOIs | |

Publication status | E-pub ahead of print - 26 Dec 2018 |

### Fingerprint

### Keywords

- math.GT
- math.DG
- 57R55, 57R50

### Cite this

**The classification of 2-connected 7-manifolds.** / Crowley, Diarmuid; Nordström, Johannes.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - The classification of 2-connected 7-manifolds

AU - Crowley, Diarmuid

AU - Nordström, Johannes

PY - 2018/12/26

Y1 - 2018/12/26

N2 - We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis. The main additional ingredient is an extension of the Eells-Kuiper invariant for any closed spin 7-manifold, regardless of whether the spin characteristic class p_M in the fourth integral cohomology of M is torsion. In addition we determine the inertia group of 2-connected M - equivalently the number of oriented smooth structures on the underlying topological manifold - in terms of p_M and the torsion linking form.

AB - We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis. The main additional ingredient is an extension of the Eells-Kuiper invariant for any closed spin 7-manifold, regardless of whether the spin characteristic class p_M in the fourth integral cohomology of M is torsion. In addition we determine the inertia group of 2-connected M - equivalently the number of oriented smooth structures on the underlying topological manifold - in terms of p_M and the torsion linking form.

KW - math.GT

KW - math.DG

KW - 57R55, 57R50

UR - http://arxiv.org/abs/1406.2226

U2 - 10.1112/plms.12222

DO - 10.1112/plms.12222

M3 - Article

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

ER -