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

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applications, one to 2-connected 7-manifolds (a new proof -- and slightly different formulation -- of an up to now unpublished Theorem by Crowley and Nordstroem and one to simply connected 7-manifolds with the cohomology ring of $S^2\times S^5♯S^3\times S^4$. 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.

that the paper has been accepted for publication by the Journal of Topology

Cited by in corpus (11)

• Notes on explicit smooth maps on 7-dimensional manifolds into the 4-dimensional Euclidean space
• Suspension homotopy of $6$-manifolds
• Loop homotopy of $6$-manifolds over $4$-manifolds
• Special generic maps and fold maps and information on triple Massey products of higher dimensional differentiable manifolds
• On the classification of certain 1-connected 7-manifolds and related problems
• 7-dimensional simply-connected spin manifolds whose integral cohomology rings are isomorphic to that of ${\mathbb{C}P}^2\times S^3$ admit round fold maps
• Mapping class group of manifolds which look like $3$-dimensional complete intersections
• Global topologies of Reeb spaces of stable fold maps with non-trivial top homology groups
• New explicit construction of fold maps on general 7-dimensional closed and simply-connected spin manifolds
• 7-dimensional closed simply-connected and spin manifolds having 2nd integral cohomology classes whose squares are not divisible by 2 and stable fold maps on them
• Free circle actions on certain simply connected $7-$manifolds