The classification of highly connected manifolds in dimensions 7 and 15

Abstract

Let P be a closed smooth (4j-2)-connected 8j-manifold. We complete Wilkens' classification of the manifolds P for j = 1,2 and give an alternative proof to Wall's classification of the manifolds for j > 2. The Hopf-invariant-one dimensions (j=1,2) are characteristed by the fact that the quadratic linking functions which classify may be inhomogeneous. Hence we also extend the classification of (homogeneous) quadratic linking forms on finite abelian groups (due to Nikulin) to the inhomogeneous case.

PhD Thesis, Indiana University 2001, 117 pages

Cited by in corpus (8)

• The classification of 2-connected 7-manifolds
• A positively curved manifold homeomorphic to T${}_1$S${}^4$
• Embedded surfaces with infinite cyclic knot group
• On the classification of 1-connected 7-manifolds with torsion free second homology
• Highly connected 7-manifolds and non-negative curvature
• Regular Circle Actions on 2-connected 7-manifolds
• Open manifolds with non-homeomorphic positively curved souls
• Kreck-Stolz invariants for quaternionic line bundles