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

Bruner, Robert; Rognes, John

doi:10.1090/tran/8680

The Adams spectral sequence for the image-of-$J$ spectrum
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by Robert R. Bruner and John Rognes PDF

Trans. Amer. Math. Soc. 375 (2022), 5803-5827 Request permission

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 [Bol. Soc. Mat. Mexicana (2) 20 (1975), pp. 6–11].

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