The classification of 2-connected 7-manifolds

Diarmuid Crowley, Johannes Nordström

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
Number of pages56
JournalProceedings of the London Mathematical Society
Early online date26 Dec 2018
DOIs
Publication statusE-pub ahead of print - 26 Dec 2018

Fingerprint

Torsion
Topological manifold
Closed
Characteristic Classes
Inertia
Linking
Cohomology
Invariant
Theorem
Form

Keywords

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

Cite this

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

In: Proceedings of the London Mathematical Society, 26.12.2018.

Research output: Contribution to journalArticle

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