2025/04/16 by Fournier-Facio, Francesco, Iveson, Harry, Harry Iveson +6
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2504.12002
openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We show that an accessible group with infinitely many ends has property R∞. That is, it has infinitely many twisted conjugacy classes for any twisting automorphism. We deduce that having property R∞ is undecidable amongst finitely presented groups. We also show that the same is true for a wide class of relatively hyperbolic groups, filling in some of the gaps in the literature. Specifically, we show that a non-elementary, finitely presented relatively hyperbolic group with finitely generated peripheral subgroups which are not themselves relatively hyperbolic, has property R∞.