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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Torsion in $ K$-theory and the Bott maps

Author: Albert T. Lundell
Journal: Trans. Amer. Math. Soc. 183 (1973), 59-85
MSC: Primary 55F45
MathSciNet review: 0326730
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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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Keywords: Bott map, spectrum, generalized cohomology, K-theory, Chern character, e-invariant
Article copyright: © Copyright 1973 American Mathematical Society

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