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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59064We 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.19 pagesAlgebraic TopologyDifferential Geometry55R15;55R40;57T35A classification of $S^3$-bundles over $S^4$text