## 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. 6β11].## References

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## Additional Information

**Robert R. Bruner**- Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan
- MR Author ID: 42485
- ORCID: 0000-0001-6699-5184
- Email: robert.bruner@wayne.edu
**John Rognes**- Affiliation: Department of Mathematics, University of Oslo, Norway
- MR Author ID: 329650
- ORCID: 0000-0002-4781-367X
- Email: rognes@math.uio.no
- Received by editor(s): July 15, 2021
- Received by editor(s) in revised form: January 1, 2600
- Published electronically: May 23, 2022
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 5803-5827 - MSC (2020): Primary 55Q50, 55T15
- DOI: https://doi.org/10.1090/tran/8680
- MathSciNet review: 4469237