Operations on resolutions and the reverse Adams spectral sequence

Blanc, David A.

doi:10.1090/S0002-9947-1994-1132432-2

Operations on resolutions and the reverse Adams spectral sequence
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Trans. Amer. Math. Soc. 342 (1994), 197-213 Request permission

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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