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arXiv · 2105.02601

The Adams spectral sequence for the image-of-$J$ spectrum

Robert R. Bruner·John Rognes
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Abstract

We show that if we factor the long exact sequence in cohomology of a cofiber sequence of spectra into short exact sequences, then the $d_2$-differential in the Adams spectral sequence of any one term is related in a precise way to Yoneda composition with the 2-extension given by the complementary terms in the long exact sequence. We use this to give a complete analysis of the Adams spectral sequence for the connective image-of-$J$ spectrum, finishing a calculation that was begun by D. Davis in 1975.

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Robert R. Bruner, John Rognes. 2021-05-06. The Adams spectral sequence for the image-of-$J$ spectrum. https://doi.org/10.1090/tran%2F8680

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