The classification of 2-connected 7-manifolds
Geometric Topology
2020-05-12 v3 Differential Geometry
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.
Cite
@article{arxiv.1406.2226,
title = {The classification of 2-connected 7-manifolds},
author = {Diarmuid Crowley and Johannes Nordström},
journal= {arXiv preprint arXiv:1406.2226},
year = {2020}
}
Comments
Corrected the definition of pseudo-isotopy of almost diffeomorphisms, 56 pages. To appear in Proc. Lond. Math. Soc