Right-angled mock reflection and mock Artin groups

Abstract

We define a right-angled mock reflection group to be a group G acting combinatorially on a CAT(O) cubical complex such that the action is simply-transitive on the vertex set and all edge-stabilizers are Z 2 . We give a combinatorial characterization of these groups in terms of graphs with local involutions. Any such graph Γ 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(π,1) space for right-angled Artin groups generalizes to these mock Artin groups.