Linear estimates for solutions of quadratic equations in free groups

2011/07/14 by Olga Kharlampovich, Kharlampovich, Olga, Alina Vdovina +1
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #advanced mathematical theories #math.GR

paper · pdf · doi:10.48550/arxiv.1107.2843

arxiv created 2011/07/14 · openalex publication_date 2011/07/14 · arxiv updated 2011/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that in a free group the length of the value of each variable in a minimal solution of a standard quadratic equation is bounded by 2s for orientable equation and by 12s⁴ for non-orientable equation, where s is the sum of the lengths of the coefficients

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