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On BP<1>*(K(Z, 3); Z/p)

Published online by Cambridge University Press:  20 November 2018

Jack Ucci
Jack Ucci*
Affiliation:
Syracuse University, Syracuse, New York
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In this paper we study the inverse limit cohomology h*(K(Z, 3)) of an Eilenberg-MacLane object K(Z, 3) for certain cohomology theories h. Our main result gives a complete description of all non-trivial differentials of the Atiyah-Hirzebruch spectral sequence (AHSS) H*(X;h*(pt)) ⇒ h*(X) for X = K(Z, 3) and h either of the complex K-theories K*( ;Z/p) and K*( ;Z(p)). This is achieved inductively using the finite symmetric product spaces SPkS3, k = pr. Identification of cycles and boundaries of each non-trivial differential leads to an explicit description of BP<1>*(K(Z, 3); Z/p) and some information about BP<1>*(K(Z, 3)).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 4 , 01 August 1983 , pp. 630 - 653
Copyright
Copyright © Canadian Mathematical Society 1983

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