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arXiv · 2208.07102

No quasi-isometric rigidity for proper actions on CAT(0) cube complexes

Francesco Fournier-Facio·Anthony Genevois
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Abstract

We exhibit a variety of groups that act properly and even cocompactly on median graphs (a.k.a. one-skeletons of CAT(0) cube complexes), with quasi-isometric groups that do not admit any proper action on a median graph. This answes a question of Niblo, Sageev and Wise. Our examples are all quasi-isometrically trivial central extensions of certain cubulated groups.

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Francesco Fournier-Facio, Anthony Genevois. 2022-08-15. No quasi-isometric rigidity for proper actions on CAT(0) cube complexes. https://arxiv.org/abs/2208.07102

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