The classification of highly connected manifolds in dimensions 7 and 15

2002/03/24 by Diarmuid Crowley, Diarmuid J. Crowley, Crowley, Diarmuid J.
Mathematics · #11E81 #57N15 #57N65 #57R22 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:11E81 #msc:57N15 #msc:57N65 #msc:57R22

paper · pdf · doi:10.48550/arxiv.math/0203253

PhD Thesis, Indiana University 2001, 117 pages

arxiv created 2002/03/24 · openalex publication_date 2002/03/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Algebraic classification of linking pairings on 3-manifolds

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