{
  "abstract": "We prove a range of rigidity results for quasiisometric embeddings between right-angled Artin groups. Among other things, we: (1) classify all self--quasiisometric-embeddings of RAAGs defined on cycles; (2) show that no $n$--dimensional RAAG is a universal receiver for quasiisometric embeddings of $n$--dimensional RAAGs. (3) prove that if the direct product $F_2^n\\times A_{C_5}^m$ can be quasiisometrically embedded in a RAAG $A_Γ$ of the same dimension, then the defining graph of $F_2^n\\times A_{C_5}^m$ must appear as an induced subgraph of $Γ$; We also establish a strong rigidity theorem for quasiisometrically embedded images of 2--flats in RAAGs defined by triangle-free graphs that are not stars, generalising a theorem of Bestvina--Kleiner--Sageev.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.12300",
  "author_total": 3,
  "authors": [
    {
      "name": "Shaked Bader"
    },
    {
      "name": "Oussama Bensaid"
    },
    {
      "name": "Harry Petyt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3prywmx0qaqad.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.12300",
  "fulltext_url": null,
  "id": "3prywmx0qaqad",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.12300",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7161054227",
  "pdf_url": "https://arxiv.org/pdf/2605.12300",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3prywmx0qaqad.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2605.12300",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.12300"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Quasiisometric embeddings between right-angled Artin groups: rigidity",
  "title_text": "Quasiisometric embeddings between right-angled Artin groups: rigidity",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/3prywmx0qaqad",
  "venue": "arXiv",
  "versions": []
}