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PreprintarXiv licencearXiv

Property R∞ for Artin and Coxeter groups whose outer automorphisms are length-preserving

  • Ignat Soroko
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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∞ 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.

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Cite

BibTeXRIS
BibTeX
@misc{soroko2026property,
  title = {{Property $R_\infty$ for Artin and Coxeter groups whose outer automorphisms are length-preserving}},
  author = {Ignat Soroko},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13904},
  eprint = {2610.13904},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13904},
}
RIS
TY  - UNPB
TI  - Property R_∞ for Artin and Coxeter groups whose outer automorphisms are length-preserving
AU  - Ignat Soroko
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13904
UR  - https://arxiv.org/abs/2610.13904
AB  - 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_∞ 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.
ER  -