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 | References | Similar Articles | Additional Information

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 . This calculation is then used to deduce that there is no space whose homotopy groups are the reduction of .

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 -modules.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1132432-2

Keywords:
Resolutions,
operations,
homology,
homotopy groups,
-algebras,
-modules,
spectral sequences

Article copyright:
© Copyright 1994
American Mathematical Society