Computing the Hopf invariant

2025/12/02 by Oleg R. Musin, Musin, Oleg R., Timur Shamazov +1
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Holomorphic and Operator Theory #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.2512.03201

Abstract

We consider Whitehead's integral formula and propose an algorithm for computing the Hopf invariant for simplicial mappings.

Citations

• Minimal simplicial spherical mappings with a given degree
• Homotopy groups and quantitative Sperner-type lemma
• Around Sperner's lemma
• Minimal Simplicial Self-maps of the 2-Sphere

Related

• Computing Invariants of Simplicial Manifolds
• A miscellany
• The monochromatic Hopf invariant
• A simplicial model for the Hopf map
• Construction of sphere maps with given degrees and a new proof of Morse index formula