Groups with arbitrary cubical dimension gap

Robert Kropholler; Chris O'Donnell

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arXiv · 1912.05055

Groups with arbitrary cubical dimension gap

Robert Kropholler·Chris O'Donnell

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Abstract

We prove that if $G = G_1\times\dots\times G_n$ acts essentially, properly and cocompactly on a CAT(0) cube complex X, then the cube complex splits as a product. We use this theorem to give various examples of groups for which the minimal dimension of a cube complex the group acts on is strictly larger than that of the minimal dimension of a CAT(0) space upon which the group acts.

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Robert Kropholler, Chris O'Donnell. 2020-02-18. Groups with arbitrary cubical dimension gap. https://arxiv.org/abs/1912.05055

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