Pith Number

pith:2DQ6XRIT

pith:2026:2DQ6XRITAVWJLJHV3R6SIOKX6P

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Quasiisometric embeddings between right-angled Artin groups: flexibility

Harry Petyt, Oussama Bensaid, Shaked Bader

Right-angled Artin groups on cycle graphs admit quasiisometric embeddings even without subgroup relations.

arxiv:2605.13314 v1 · 2026-05-13 · math.GR · math.MG

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Claims

C1strongest claim

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.

C2weakest assumption

The underlying graphs are cycles (or more generally graphs whose products are taken over cycles) and the vertex groups are finite or cyclic; the proofs rely on the combinatorial structure of these specific graphs.

C3one line summary

Complete characterization of quasiisometric embeddings between RAAGs on cycle graphs, including exotic cases without subgroup relations and hyperbolic plane embeddings into certain RAAGs.

References

300 extracted · 300 resolved · 0 Pith anchors

[1] and Osin, Denis , TITLE = 2019 · doi:10.2140/agt.2019.19.1747

[2] Abbott, Carolyn and Behrstock, Jason , TITLE =. Groups Geom. Dyn. , FJOURNAL =. 2023 , NUMBER =. doi:10.4171/ggd/722 , URL = 2023 · doi:10.4171/ggd/722

[3] Abbott, Carolyn and Behrstock, Jason and Durham, Matthew G. , TITLE =. Trans. Amer. Math. Soc. Ser. B , FJOURNAL =. 2021 , PAGES =. doi:10.1090/btran/50 , URL = 2021 · doi:10.1090/btran/50

[4] Abbott, Carolyn and Behrstock, Jason and Russell, Jacob , TITLE =. J. Topol. Anal. , FJOURNAL =. 2025 , NUMBER =. doi:10.1142/S1793525323500516 , URL = 2025 · doi:10.1142/s1793525323500516

[5] Abbott, Carolyn R. and Dahmani, Fran. Property. Math. Z. , FJOURNAL =. 2019 , NUMBER =. doi:10.1007/s00209-018-2094-1 , URL = 2019 · doi:10.1007/s00209-018-2094-1

Receipt and verification

First computed	2026-05-18T02:44:48.813656Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0e1ebc513056c95a4f5dc7d243957f3f24c9b2b9887486c16cd49e2a85e5c65

Aliases

arxiv: 2605.13314 · arxiv_version: 2605.13314v1 · doi: 10.48550/arxiv.2605.13314 · pith_short_12: 2DQ6XRITAVWJ · pith_short_16: 2DQ6XRITAVWJLJHV · pith_short_8: 2DQ6XRIT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2DQ6XRITAVWJLJHV3R6SIOKX6P \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d0e1ebc513056c95a4f5dc7d243957f3f24c9b2b9887486c16cd49e2a85e5c65

Canonical record JSON

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    "abstract_canon_sha256": "da6ea93a7f9d33db6e04d4930cf34a8360268d86adf3ddf09ced8fb2725f2644",
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      "math.MG"
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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-13T10:26:23Z",
    "title_canon_sha256": "7a872cd6ec50825a670b7e2b79db8478d3cfe6ab8191b6bd2a3fa4edd78f439c"
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