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

Ajay Raj, Tibor Macko (2024)

Archivum Mathematicum

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.

On the exponent of the cokernel of the forget-control map on K₀-groups

Francis X. Connolly, Stratos Prassidis (2002)

Fundamenta Mathematicae

For groups that satisfy the Isomorphism Conjecture in lower K-theory, we show that the cokernel of the forget-control K₀-groups is composed by the NK₀-groups of the finite subgroups. Using this information, we can calculate the exponent of each element in the cokernel in terms of the torsion of the group.

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