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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
DOI: https://doi.org/10.1090/S0002-9947-1994-1132432-2
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, <IMG WIDTH="21" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\Pi$">-algebras, <IMG WIDTH="18" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$\pi$">-modules, spectral sequences
Article copyright: © Copyright 1994 American Mathematical Society