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Keywords:
vector bundle; sphere bundle over sphere; microbundle; homotopy equivalence; homeomorphism; surgery; characteristic class
vector bundle; sphere bundle over sphere; microbundle; homotopy equivalence; homeomorphism; surgery; characteristic class
Summary:
We calculate the structure sets in the sense of surgery theory of total spaces of bundles over eight-dimensional sphere with fibre a seven-dimensional sphere, in which manifolds homotopy equivalent to the total spaces are organized, and we investigate the question, which of the elements in these structure sets can be realized as such bundles.
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