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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

BP torsion in finite $ H$-spaces


Author: Richard Kane
Journal: Trans. Amer. Math. Soc. 264 (1981), 473-497
MSC: Primary 55P45; Secondary 55N22
MathSciNet review: 603776
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Abstract: Let $ p$ be odd and $ (X,\mu )$ a $ 1$-connected $ \operatorname{mod} p$ finite $ H$-space. It is shown that for $ n \geqslant 1$ the Morava $ K$-theories, $ k{(n)_ \ast }(X)$ and $ k{(n)^ \ast }(X)$, have no higher $ {\upsilon _n}$ torsion. Also examples are constructed to show that $ {\upsilon _1}$ torsion in $ BP{\langle 1\rangle ^ \ast }(X)$ can be of arbitrarily high order.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0603776-6
PII: S 0002-9947(1981)0603776-6
Keywords: Finite $ H$-spaces, $ k(n)$ homology, cohomology operations, Eilenberg-Moore spectral sequence, Hopf algebra
Article copyright: © Copyright 1981 American Mathematical Society