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PreprintCC BY-NC-SA 4.0arXiv

Indecomposable Uniform Families on the Adams 4-Line

  • Jordan Benson
  • Runji Li
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Abstract

We show that the fj, pj, D3(j), and pj' families on the 4-line of the classical Adams spectral sequence all conform to the Uniform Doomsday Conjecture. We do so by first using Bruner's formula to establish uniform families of differentials on these classes. We then study the Burklund-Xu and Cartan-Eilenberg spectral sequences to ensure that the differential targets are nonzero. The fj family requires further analysis of possible Adams d2 differentials since the fj support uniform d3 differentials. As a result of our work, only two indecomposable Sq0 families remain to be settled in Adams filtration 4.

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Cite

BibTeXRIS
BibTeX
@misc{benson2026indecomposable,
  title = {{Indecomposable Uniform Families on the Adams 4-Line}},
  author = {Jordan Benson and Runji Li},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02614},
  eprint = {2611.02614},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02614},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Indecomposable Uniform Families on the Adams 4-Line
AU  - Jordan Benson
AU  - Runji Li
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02614
UR  - https://arxiv.org/abs/2611.02614
AB  - We show that the f_j, p_j, D_3(j), and p_j' families on the 4-line of the classical Adams spectral sequence all conform to the Uniform Doomsday Conjecture. We do so by first using Bruner's formula to establish uniform families of differentials on these classes. We then study the Burklund-Xu and Cartan-Eilenberg spectral sequences to ensure that the differential targets are nonzero. The f_j family requires further analysis of possible Adams d_2 differentials since the f_j support uniform d_3 differentials. As a result of our work, only two indecomposable Sq^0 families remain to be settled in Adams filtration 4.
ER  -