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

2012/06/22 by Camp, Wes, Mihalik, Michael
#20F65 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1206.5234

Abstract

If (W,S) is a right-angled Coxeter system and W has no \mathbb Z³ 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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