The classification of highly connected manifolds in dimensions 7 and 15

Details The classification of highly connected manifolds in dimensions 7 and 15 The classification of highly connected manifolds in dimensions 7 and 15

2002-03-24

arxiv.org/abs/math/0203253v1

Mathematics

Geometric Topology

PhD Thesis, Indiana University 2001, 117 pages

Scientific paper

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.

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