English

On essential simplicial maps $S^3 \rightarrow S^2$

Algebraic Topology 2025-12-10 v1

Abstract

A fiber-uniform bound on the complexity of an essential simplicial map S3S2S^3\rightarrow S^2 is proven, and the tightness of the bound is investigated. It follows that the triangulation of the Hopf map constructed by Madahar and Sarkaria is minimal in its homotopy class in terms of the number of 3-simplices in the triangulation of S3S^3.

Keywords

Cite

@article{arxiv.2512.08584,
  title  = {On essential simplicial maps $S^3 \rightarrow S^2$},
  author = {Mikhail V. Bludov and Sergei Vad. Fomin and Oleg R. Musin},
  journal= {arXiv preprint arXiv:2512.08584},
  year   = {2025}
}

Comments

6 pages

R2 v1 2026-07-01T08:16:57.719Z