The classification of 2-connected 7-manifolds

Diarmuid Crowley, Johannes Nordström

Research output: Contribution to journalArticlepeer-review

9 Citations (SciVal)


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
Pages (from-to)1-54
Number of pages54
JournalProceedings of the London Mathematical Society
Issue number1
Early online date26 Dec 2018
Publication statusPublished - 26 Dec 2018


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


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