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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Operations on resolutions and the reverse Adams spectral sequence

Author: David A. Blanc
Journal: Trans. Amer. Math. Soc. 342 (1994), 197-213
MSC: Primary 55T15; Secondary 18G10
MathSciNet review: 1132432
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Abstract: We describe certain operations on resolutions in abelian categories, and apply them to calculate part of a reverse Adams spectral sequence, going "from homotopy to homology", for the space $ {\mathbf{K}}(\mathbb{Z}/2,n)$. This calculation is then used to deduce that there is no space whose homotopy groups are the reduction $ \bmod \; 2$ of $ {\pi _\ast}{{\mathbf{S}}^r}$.

As another application of the operations we give a short proof of T. Y. Lin's theorem on the infinite projective dimension of all nonfree $ \pi $-modules.

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Keywords: Resolutions, operations, homology, homotopy groups, $ \Pi $-algebras, $ \pi $-modules, spectral sequences
Article copyright: © Copyright 1994 American Mathematical Society