On manifolds homotopy equivalent to the total spaces of $S^7$-bundles over $S^8$

Raj, Ajay ; Macko, Tibor

Archivum mathematicum, Tome 60 (2024) no. 3, pp. 125-134

Abstract (VO)

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.

Détail

DOI : 10.5817/AM2024-3-125

Classification : 19J25, 55R25, 55R40, 57N55
Keywords: vector bundle; sphere bundle over sphere; microbundle; homotopy equivalence; homeomorphism; surgery; characteristic class

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