Free groups are L²-subgroup rigid

2024/03/14 by Andrei Jaikin‐Zapirain, Jaikin-Zapirain, Andrei · 3 citations
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2403.09515

openalex publication_date 2024/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we introduce the notion of L²-subgroup rigid groups and demonstrate that free groups are L²-subgroup rigid. As a consequence, we establish the equivalence between compressibility, inertness, strong inertness, and L²-independence for a finitely generated subgroup of a free group, confirming a conjecture by Dicks and Ventura as well as the one by Antolin and Jaikin-Zapirain.

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• Universal L²-torsion and sutured decomposition for 3-manifolds
• Exposure Orders in Free Group Algebras: Minimal Schreier Transversals, Free Bases, and Gröbner Bases
• On the asymptotic equidistribution of word values in symmetric groups

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