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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].


Algebraic Geometry | Geometry and Topology


Author's Accepted Manuscript. First published in Trans. Amer. Math. Soc. 375 (2022), 5803-5827 (online 23 May 2022), published by the American Mathematical Society. © 2022 American Mathematical Society.