On the relation of connective K-theory to homology
Published online by Cambridge University Press: 24 October 2008
Extract
Let us denote by k*( ) the homology theory determined by the connective BU spectrum, bu, that is, in the notations of (1) and (9), bu2n = BU(2n,…,∞), bu2n+1 = U(2n + 1,…, ∞) with the spectral maps induced via Bott periodicity. The resulting spectrum, bu, is a ring spectrum. Recall that k*(point) ≅ Z[t], degree t = 2. There is a natural transformation of ring spectra
inducing a morphism
of homology functors. It is the objective of this note to establish: Theorem. Let X be a finite complex. Then there is a natural exact sequence
where Z is viewed as a Z[t] module via the augmentation
and, is induced by η*in the natural way.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 3 , November 1970 , pp. 637 - 639
- Copyright
- Copyright © Cambridge Philosophical Society 1970
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