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Coarse cubical rigidity

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Fioravanti,  Elia       
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Fioravanti, E., Levcovitz, I., & Sageev, M. (2024). Coarse cubical rigidity. Journal of Topology, 17(3): e12353. doi:10.1112/topo.12353.


Cite as: https://hdl.handle.net/21.11116/0000-000F-BB66-C
Abstract
We show that for many right-angled Artin and Coxeter groups, all cocompact cubulations coarsely look the same: They induce the same coarse median structure on the group. These are the first examples of non-hyperbolic groups with this property. For all graph products of finite groups and for Coxeter groups with no irreducible affine parabolic subgroups of rank $\geq 3$ , we show that all automorphisms preserve the coarse median structure induced, respectively, by the Davis complex and the Niblo–Reeves cubulation. As a consequence, automorphisms of these groups have nice fixed subgroups and satisfy Nielsen realisation.