The asymptotic geometry of right-angled Artin groups, I

By M. Bestvina, Bruce Kleiner, Michah Sageev. 2007

66 citations recorded by the source corpus.

We study atomic right-angled Artin groups ‐ those whose defining graph has no cycles of length 4, and no separating vertices, separating edges, or separating vertex stars. We show that these groups are not quasi-isometrically rigid, but that an intermediate form of rigidity does hold. We deduce from this that two atomic groups are quasi-isometric iff they are isomorphic. 20F65, 20F69; 20F67, 05C25

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fb9800656594aaa37fc6d1e9bb1cc6e86eab7d0c

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In Applied Mathematics

1. Anne Thomas
2. Pallavi Dani
3. Anthony Genevois
4. Alexandre Martin

In Geometry and Topology

1. Anne Thomas
2. Pallavi Dani
3. Anthony Genevois
4. Alexandre Martin
5. Hung Cong Tran

Citations in the corpus

• Automorphisms of graph products of groups from a geometric perspective (2018, methodology): “This description of the automorphism group in Theorem B simplifies further in the case where Γ is in addition assumed not to contain any separating star (following [BKS08], a finite connected graph without vertex of valence < 2, whose girth is at least 5, and that does not contain separating stars i”
• Divergence in right-angled Coxeter groups (2012, result): “8 of [6], concerning right-angled Artin groups, and neither of these results can be applied here.”