Coxeter Groups act on CAT(0) cube complexes

By Graham A. Niblo, Lawrence Reeves. 2003

129 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0c3c815138ae9283dd9915b9cff3d5afba0b20c1

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In Discrete Mathematics and Combinatorics

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Citations in the corpus

Weak hyperbolicity of cube complexes and quasi‐arboreal groups (2011, background): “(4) Finitely generated Coxeter groups act properly on CAT(0) cube complexes with finitely many orbits of hyperplanes [28].”
Coxeter groups are virtually special (2010, methodology): “We will certainly be relying on the details of his construction and refer the reader to [21,7,19,4,12] and especially [18] for the case of Coxeter groups.”
Cubulating spaces with walls (2003, methodology): “Some of the papers cited above ([11], [7], [9]) take the point of view that the primitive data for constructing a CAT(0) cube complex is a partially ordered set with an order-reversing involution, with certain discreteness and nesting assumptions a la Dunwoody, which is to become the system of halfs”
Hereditary conjugacy separability of right angled Artin groups and its applications (2009, background): “In the case when G is right angled or word hyperbolic (in Gromov’s sense [27]), Niblo and Reeves proved that the action of G on C is cocompact (see [45]).”
RESEARCH ANNOUNCEMENT: THE STRUCTURE OF GROUPS WITH A QUASICONVEX HIERARCHY (2009, background): “Some further work along these lines is: Cubulation of Coxeter groups [34], of certain small-cancellation groups [49], of Gromov’s random groups at density < 16 [37], and of rhombus groups related to Penrose tilings [29].”
Finiteness properties of cubulated groups (2012, methodology): “We give conditions similar to the Parallel Wall Separation Condition of Brink–Howlett that was used by Niblo–Reeves to prove local finiteness of their cubulations of Coxeter groups [BH93, NR03].”
Cubulating random groups at density less than 1/6 (2011, unknown): “Niblo and Reeves [NR03] and Wise [Wis04] had observed that Sageev’s construction works in the context of “geometric spaces with walls”.”
Packing subgroups in relatively hyperbolic groups (2006, background): “ion of a group G on a CAT(0) cube complex C gives rise to natural subgroups of G with bounded packing. These subgroups arise as stabilizers of hyperplanes in C. 1.2 Pairwise close spaces Niblo–Reeves [13] proved that given n, κ, D and δ there exists M = M(n,κ,D,δ) such that the following thinness co”
Some geometric groups with Rapid Decay (2003, background): “t depends on the geodesic we started with) has at most npieces. In particular, since Coxeter groups are known to act properly discontinuously by isometries on CAT(0) cube complexes of ﬁnite dimension [25], we have the following corollary. Corollary 4.9. Coxeter groups have property RD. Corollary 0.6”
Special Cube Complexes (2008, methodology): “For instance, in [ NR ] his construction is used to show that word-hyperbolic Coxeter groups act properly discontinuously and cocompactly on CAT(0) cube complexes, and the same is shown for finitely presented C � (1/6) small-cancellation groups in [Wi6].”
The Geometry and Topology of Coxeter Groups (2025, methodology): “The construction of [228] comes from Sageev [251].”