Property $R_\infty$ for Artin and Coxeter groups whose outer automorphisms are length-preserving
Year: 2026
Type: preprint
Abstract: We prove that every length-preserving automorphism of a nonspherical Artin or Coxeter group has infinite Reidemeister number. As a consequence, we establish property $R_\infty$ for large-type free-of-infinity Artin groups, infinite strongly rigid Coxeter groups, and infinite virtually abelian Coxeter groups, including all affine Coxeter groups. We also prove that the automorphism group of every infinite irreducible non-affine strongly rigid Coxeter group is acylindrically hyperbolic.
Source: arXiv (Cornell University)
Author: Soroko, Ignat
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221524394