Classifies smooth closed oriented manifolds homotopy equivalent to three families of sphere products up to almost diffeomorphism by realizing the image of the normal-invariant map with explicit constructions from bundles and plumbings.
A classification of $S^3$-bundles over $S^4$
1 Pith paper cite this work. Polarity classification is still indexing.
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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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Smooth manifolds homotopy equivalent to products of spheres
Classifies smooth closed oriented manifolds homotopy equivalent to three families of sphere products up to almost diffeomorphism by realizing the image of the normal-invariant map with explicit constructions from bundles and plumbings.