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The invariant cell number property for 𝔼4-rings

  • Anish Chedalavada
  • Florian Riedel
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Abstract

For any non-zero 𝔼4-ring R, we prove that an n-fold direct sum of suspensions of R cannot admit an exhaustive filtration by fewer than n cells. We do this by showing that certain integral representations of the symmetric group lift to Schur functors on additively 𝔼3-monoidal ∞-categories. We then reduce the statement to a vanishing fact for rational Schur functors due to Deligne.

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Cite

BibTeXRIS
BibTeX
@misc{chedalavada2026invariant,
  title = {{The invariant cell number property for $\mathbbE_4$-rings}},
  author = {Anish Chedalavada and Florian Riedel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22162},
  eprint = {2610.22162},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22162},
}
RIS
TY  - UNPB
TI  - The invariant cell number property for 𝔼_4-rings
AU  - Anish Chedalavada
AU  - Florian Riedel
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22162
UR  - https://arxiv.org/abs/2610.22162
AB  - For any non-zero 𝔼_4-ring R, we prove that an n-fold direct sum of suspensions of R cannot admit an exhaustive filtration by fewer than n cells. We do this by showing that certain integral representations of the symmetric group lift to Schur functors on additively 𝔼_3-monoidal ∞-categories. We then reduce the statement to a vanishing fact for rational Schur functors due to Deligne.
ER  -