English

A classification of $S^3$-bundles over $S^4$

Algebraic Topology 2007-05-23 v1 Differential Geometry

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.

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Cite

@article{arxiv.math/0004147,
  title  = {A classification of $S^3$-bundles over $S^4$},
  author = {Diarmuid Crowley and Christine M. Escher},
  journal= {arXiv preprint arXiv:math/0004147},
  year   = {2007}
}

Comments

19 pages

R2 v1 2026-07-22T16:32:22.529Z