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On Adams' splitting of K-theory and complex cobordism
Published online by Cambridge University Press: 24 October 2008
Extract
In (2) Adams gave a splitting of complex K-theory with coefficients in the ring R(d) of rationals a/b such that b contains no prime p with p ≡ 1 (mod d). The splitting comes from a complete set of projection operators on K(X; R(d)). One of the operators is then used to obtain a stable, multiplicative idempotent ε on complex cobordism with coefficients in the same ring R(d) and hence a splitting of the representing spectrum MUR(d). However, the idempotent is initially defined over the rational numbers and work is needed to show that it actually gives an operation on MUR(d). Since Novikov (6) has shown that multiplicative cobordism operations are distinguished by their values on the generator ω ∈ MU2CP∞, it is natural to seek an explicit formula for ε(ω) which wi11 show that ε gives an operation over the subring R(d).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 1 , January 1978 , pp. 113 - 116
- Copyright
- Copyright © Cambridge Philosophical Society 1978