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On Adams' splitting of K-theory and complex cobordism

Published online by Cambridge University Press:  24 October 2008

Idar Hansen
Affiliation:
University of Kentucky

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
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

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