Right-angled Mock Reflection and Mock Artin Groups
نویسنده
چکیده
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 Z2. 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.
منابع مشابه
Actions of right-angled Artin groups in low dimensions
We survey the role of right-angled Artin groups in the theory of diffeomorphism groups of low dimensional manifolds. We first describe some of the subgroup structure of right-angled Artin groups. We then discuss the interplay between algebraic structure, compactness, and regularity for group actions on one–dimensional manifolds. For compact one–manifolds, every right-angled Artin group acts fai...
متن کامل2 00 6 On the profinite topology of right - angled Artin groups
In the present work, we give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Also, we show that right-angled Artin groups are conjugacy separable. Moreover, we investigate the profinite topology of F 2 × F 2 and of the group L in [22], which are the only obstructions for the subgroup separability of th...
متن کاملSe p 20 06 On the profinite topology of right - angled Artin groups
In the present work, we give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Also, we show that right-angled Artin groups are conjugacy separable. Moreover, we investigate the profinite topology of F 2 × F 2 and of the group L in [22], which are the only obstructions for the subgroup separability of th...
متن کاملCryptography with right-angled Artin groups
In this paper we propose right-angled Artin groups as platform for a secret sharing scheme based on the efficiency (linear time) of the word problem. We define two new problems: subgroup isomorphism problem for Artin subgroups and group homomorphism problem in right-angled Artin groups. We show that the group homomorphism and graph homomorphism problems are equivalent, and the later is known to...
متن کاملEmbeddings of graph braid and surface groups in right-angled Artin groups and braid groups
We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to rightangled Artin groups a result of Lyndon for free gr...
متن کامل