The classification of 2-connected 7-manifolds

Diarmuid Crowley; Johannes Nordström

doi:10.1112/plms.12222

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arXiv · 1406.2226

The classification of 2-connected 7-manifolds

Diarmuid Crowley·Johannes Nordström

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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.

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Diarmuid Crowley, Johannes Nordström. 2014-06-09. The classification of 2-connected 7-manifolds. https://doi.org/10.1112/plms.12222

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