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

摘要

We generalize a result [Kreck, Ann of Math. (2) 149 (1999) 707-754; Theorem 6] 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concrete applications, one to 2-connected 7-manifolds (a new proof and slightly different formulation of an up to now unpublished Theorem by [Crowley and Nordstrom, Preprint, 2014, arXiv: 1406.2226]) and one to simply connected 7-manifolds with the cohomology ring of S2xS5S3xS4. 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.