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Rational BP operations and the Chern character

Published online by Cambridge University Press:  24 October 2008

Richard Kane
Richard Kane
Affiliation:
University of Alberta
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Extract

This paper will study certain rational BP operations. We will work in the category of spaces having the homotopy type of CW complexes. Recall that for − 1 ≤ n ≤ ∞ there is defined in this category the homology theory BP(n)*(X). (See (7).) In particular, BP(∞)*(X) = BP*(X) is the usual Brown Peterson homology of X, BP(1)*(X) = l*(X) is the canonical direct summand of connective K-theory with Qp coefficients (Qp are the integers localized at the prime p), BP(0)*(X) = Hℤ*(X) is ordinary homology with Qp coefficients, and BP(−1)*(X) = Hℤ/p*(X) is ordinary homology with ℤp coefficients (ℤp are the integers reduced mod p). For 1 ≤ n ≤ ∞, BP(n)*(X) is a module over BP(n)*(pt) = Qp[v1, …, vn] (deg vs = 2ps − 2). The BP(n) theories are all related via canonical maps p(m, n):BP(m)*(X) → BP(n)*(X) whose performance is described in (7).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 65 - 72
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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