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A decomposition is given of the S-type of the classifying spaces of the classical groups. This decomposition is in terms of Thom spaces and by means of it cobordism groups are embedded into the stable homotopy of classifying spaces. This is used to show that each of the classica…
There is a homomorphism from the stable homotopy of the classifying space of the group of units in a ring to its algebraic [italic]K-theory. When the ring has enough roots of unity a "Bott element" exists in these groups (taken with coefficients). We compute the groups obtained …
