On essential simplicial maps S³ → S²

2025/12/09 by Bludov, Mikhail V., Fomin, Sergei Vad., Musin, Oleg R.
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · doi:10.48550/arxiv.2512.08584

openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

Abstract

A fiber-uniform bound on the complexity of an essential simplicial map S³→ S² 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 S³.

Citations

• Homotopy groups and quantitative Sperner-type lemma

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