The Hurwitz Equivalence Problem is Undecidable

2005/11/07 by E. Liberman, Eran Liberman, Liberman, E. +3
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #Logic, programming, and type systems #Polynomial and algebraic computation #math.AG #math.LO

paper · pdf · doi:10.48550/arxiv.math/0511153

arxiv created 2005/11/07 · openalex publication_date 2005/11/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that the Hurwitz equivalence problem for 1-factorizations in F₂ ⊕ F₂ is undecidable, and as a consequence, the Hurwitz equivalence problem for Δ²-factorizations in the braid groups B_n, n≥ 5 is also undecidable.

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• Graph Theoretic Method for Determining non Hurwitz Equivalence in the Braid Group and Symmetric group
• Hurwitz Equivalence of Braid Group Factorizations Consisting of a Semi-Frame
• Properties of Hurwitz Equivalence in the Braid Group of Order n
• Hurwitz Equivalence in Braid Group B₃
• Factorizations in finite groups