The classification of 2-connected 7-manifolds

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.

Corrected the definition of pseudo-isotopy of almost diffeomorphisms, 56 pages. To appear in Proc. Lond. Math. Soc

References in corpus (4)

• Obstruction theory on 8-manifolds
• On the classification of 1-connected 7-manifolds with torsion free second homology
• Partial restoration of chiral symmetry in a confining string
• Computations and Applications of eta invariants

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