A classification of S³-bundles over S⁴

2000/04/24 by Diarmuid Crowley, Crowley, Diarmuid, Christine M. Escher +2 · 2 citations
Mathematics · Medicine · #55R15 #55R40 #57T35 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #math.AT #math.DG #msc:55R15 #msc:55R40 #msc:57T35

paper · pdf · doi:10.48550/arxiv.math/0004147

19 pages

arxiv created 2000/04/24 · openalex publication_date 2000/04/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the total spaces of bundles over the four sphere with fiber a three sphere up to orientation preserving and reversing homotopy equivalence, homeomorphism and diffeomorphism. These total spaces have been of interest to both topologists and geometers. It has recently been shown by Grove and Ziller that each of these total spaces admits metrics with nonnegative sectional curvature.

Cited by

• Homotopy classification of S^2k-1-bundles over S^2k
• Complexes equivalent to S^2k-1-fibrations over S^2k

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