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Quasiisometric embeddings between right-angled Artin groups: flexibility

  • Shaked Bader
  • Oussama Bensaid
  • Harry Petyt
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Abstract

We give a complete characterisation of when the right-angled Artin group on one cycle graph can be quasiisometrically embedded in the right-angled Artin group on another cycle graph. In particular, we find infinitely many instances of quasiisometric embeddings where there is no subgroup relation. This contrasts with the fact that such groups are quasiisometrically rigid. More generally, we construct quasiisometric embeddings between graph products of finite or cyclic groups whose underlying graphs are cycles. As a special case, we obtain exotic quasiisometric embeddings of the hyperbolic plane in all right-angled Artin groups whose defining graph contains an induced cycle of length greater than four.

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Cite

BibTeXRIS
BibTeX
@misc{bader2026quasiisometric,
  title = {{Quasiisometric embeddings between right-angled Artin groups: flexibility}},
  author = {Shaked Bader and Oussama Bensaid and Harry Petyt},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.13314},
  eprint = {2605.13314},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.13314},
}
RIS
TY  - UNPB
TI  - Quasiisometric embeddings between right-angled Artin groups: flexibility
AU  - Shaked Bader
AU  - Oussama Bensaid
AU  - Harry Petyt
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2605.13314
UR  - https://arxiv.org/abs/2605.13314
AB  - We give a complete characterisation of when the right-angled Artin group on one cycle graph can be quasiisometrically embedded in the right-angled Artin group on another cycle graph. In particular, we find infinitely many instances of quasiisometric embeddings where there is no subgroup relation. This contrasts with the fact that such groups are quasiisometrically rigid. More generally, we construct quasiisometric embeddings between graph products of finite or cyclic groups whose underlying graphs are cycles. As a special case, we obtain exotic quasiisometric embeddings of the hyperbolic plane in all right-angled Artin groups whose defining graph contains an induced cycle of length greater than four.
ER  -