Right-angled mock reflection and mock Artin groups

Scott, Richard

doi:10.1090/S0002-9947-08-04452-8

Right-angled mock reflection and mock Artin groups
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Trans. Amer. Math. Soc. 360 (2008), 4189-4210 Request permission

Abstract:

We define a right-angled mock reflection group to be a group $G$ acting combinatorially on a CAT($0$) cubical complex such that the action is simply-transitive on the vertex set and all edge-stabilizers are $\mathbb Z_2$. We give a combinatorial characterization of these groups in terms of graphs with local involutions. Any such graph $\Gamma$ not only determines a mock reflection group, but it also determines a right-angled mock Artin group. Both classes of groups generalize the corresponding classes of right-angled Coxeter and Artin groups. We conclude by showing that the standard construction of a finite $K(\pi ,1)$ space for right-angled Artin groups generalizes to these mock Artin groups.

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