A classification of right-angled Coxeter groups with no 3-flats and locally connected boundary

Wes Camp; Michael Mihalik

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arXiv · 1206.5234

A classification of right-angled Coxeter groups with no 3-flats and locally connected boundary

Wes Camp·Michael Mihalik

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Abstract

If $(W,S)$ is a right-angled Coxeter system and $W$ has no $\mathbb Z^3$ subgroups, then it is shown that the absence of an elementary separation property in the presentation diagram for $(W,S)$ implies all CAT(0) spaces acted on geometrically by $W$ have locally connected CAT(0) boundary. It was previously known that if the presentation diagram of a general right-angled Coxeter system satisfied the separation property then all CAT(0) spaces acted on geometrically by $W$ have non-locally connected boundary. In particular, this gives a complete classification of the right-angled Coxeter groups with no 3-flats and with locally connected boundary.

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Wes Camp, Michael Mihalik. 2012-06-22. A classification of right-angled Coxeter groups with no 3-flats and locally connected boundary. https://arxiv.org/abs/1206.5234

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