Torsion in 𝐾-theory and the Bott maps

Lundell, Albert T.

doi:10.1090/S0002-9947-1973-0326730-6

Torsion in $K$-theory and the Bott maps
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Trans. Amer. Math. Soc. 183 (1973), 59-85 Request permission

Abstract:

The nonstable Bott maps $b{’_n}:U(n) \to {\Omega ^2}U(n + 1)$ for the unitary group are studied as to their behavior under iteration. They are then used to define and compute the coefficients of a spectrum. The corresponding cohomology theory is developed and compared with reduced complex K-theory. In this context the Chern character is induced by a map of spectra. The complex e-invariant appears as a coboundary in the long exact sequence of a cofibration.

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