On the classification of 1-connected 7-manifolds with torsion free second homology

Matthias Kreck

doi:10.1112/topo.12063

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arXiv · 1805.02391

On the classification of 1-connected 7-manifolds with torsion free second homology

Matthias Kreck

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Abstract

We generalize a result of the author about the classification of 1-connected 7-manifolds and demonstrate its use by two concrete applications, one to 2-connected 7-manifolds (a new proof -- and slightly different formulation -- of an up to now unpublished Theorem by Crowley and Nordstroem and one to simply connected 7-manifolds with the cohomology ring of $S^2 \times S^5 \sharp S^3 \times S^4$. The answer is in terms of generalized Kreck-Stolz invariants, which in the case of 2-connected 7-manifolds is equivalent to a quadratic refinement of the linking form and a generalized Eells-Kuiper invariant.

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Matthias Kreck. 2018-05-07. On the classification of 1-connected 7-manifolds with torsion free second homology. https://doi.org/10.1112/topo.12063

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