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.
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