Quasiisometric embeddings between right-angled Artin groups: rigidity
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911675678982144 |
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| author | Bader, Shaked Bensaid, Oussama Petyt, Harry |
| author_facet | Bader, Shaked Bensaid, Oussama Petyt, Harry |
| contents | By introducing branching conditions on the defining graph, we prove a range of rigidity results for quasiisometric embeddings between right-angled Artin groups. The starting point for these is that, under mild conditions on the codomain, the branching conditions imply that a quasiisometric embedding induces an embedding between the associated extension graphs. Among other things, we:
(1) provide obstructions to the existence of quasiisometric embeddings into products of trees;
(2) prove that if the direct product $F_2^n\times A_{C_5}^m$ can be quasiisometrically embedded in a RAAG of the same dimension, then this can be seen from its defining graph;
(3) classify all self--quasiisometric-embeddings of RAAGs defined on cycles;
(4) show that no $n$--dimensional RAAG is a universal receiver for quasiisometric embeddings of $n$--dimensional RAAGs.
We also establish a strong rigidity theorem for the quasiisometric images of 2--flats in RAAGs defined by triangle-free graphs that are not stars, generalising a theorem of Bestvina--Kleiner--Sageev. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12300 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasiisometric embeddings between right-angled Artin groups: rigidity Bader, Shaked Bensaid, Oussama Petyt, Harry Group Theory Metric Geometry By introducing branching conditions on the defining graph, we prove a range of rigidity results for quasiisometric embeddings between right-angled Artin groups. The starting point for these is that, under mild conditions on the codomain, the branching conditions imply that a quasiisometric embedding induces an embedding between the associated extension graphs. Among other things, we: (1) provide obstructions to the existence of quasiisometric embeddings into products of trees; (2) prove that if the direct product $F_2^n\times A_{C_5}^m$ can be quasiisometrically embedded in a RAAG of the same dimension, then this can be seen from its defining graph; (3) classify all self--quasiisometric-embeddings of RAAGs defined on cycles; (4) show that no $n$--dimensional RAAG is a universal receiver for quasiisometric embeddings of $n$--dimensional RAAGs. We also establish a strong rigidity theorem for the quasiisometric images of 2--flats in RAAGs defined by triangle-free graphs that are not stars, generalising a theorem of Bestvina--Kleiner--Sageev. |
| title | Quasiisometric embeddings between right-angled Artin groups: rigidity |
| topic | Group Theory Metric Geometry |
| url | https://arxiv.org/abs/2605.12300 |