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PreprintCC BY 4.0arXiv

On simplicial maps with non-zero Hopf invariant

  • Sergei Vad. Fomin
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Abstract

In general, it is interesting to investigate the complexity of simplicial maps under various topological constraints. In this paper, we consider maps between (triangulated oriented rational homology) manifolds with non-zero Hopf invariant and establish bounds on the simplicial complexity of the fiber of a regular point. The lower bound, which is cubic in the dimension, is proved via a refinement of a theorem of S. Eilenberg. The upper bound is notable in that it is uniform with respect to the Hopf invariant.

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Cite

BibTeXRIS
BibTeX
@misc{fomin2026simplicial,
  title = {{On simplicial maps with non-zero Hopf invariant}},
  author = {Sergei Vad. Fomin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25562},
  eprint = {2610.25562},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25562},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On simplicial maps with non-zero Hopf invariant
AU  - Sergei Vad. Fomin
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25562
UR  - https://arxiv.org/abs/2610.25562
AB  - In general, it is interesting to investigate the complexity of simplicial maps under various topological constraints. In this paper, we consider maps between (triangulated oriented rational homology) manifolds with non-zero Hopf invariant and establish bounds on the simplicial complexity of the fiber of a regular point. The lower bound, which is cubic in the dimension, is proved via a refinement of a theorem of S. Eilenberg. The upper bound is notable in that it is uniform with respect to the Hopf invariant.
ER  -