Publication Title

Geometriae Dedicata

Document Type

Article

Department or Program

Mathematics

Publication Date

3-19-2026

Abstract

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∞.

Comments

Original version is available from the publisher at: https://doi.org/10.1007/s10711-026-01078-x

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright Note

© The Author(s) 2026

Required Publisher's Statement

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

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