Bestvina-Brady groups arise as kernels of length homomorphisms GΓ → Z from right-angled Artin groups to the integers. Under some connectivity assumptions on the flag complex ∆Γ, we compute several algebraic invariants of such a group NΓ, directly from the underlying graph Γ. As an application, we give examples of finitely presented Bestvina-Brady groups which are not isomorphic to any Artin gro...

We show that given a collection $$X=\{f_1$$ , ..., $$f_m\}$$ of pure mapping classes on surface S, there is an explicit constant N, depending only X, such their Nth powers $$\{f_1^N$$ $$f_m^N\}$$ generate the expected right-angled Artin subgroup MCG(S). Moreover, we these subgroups are undistorted, and each element pseudo-Anosov largest possible subsurface.

We observe that, for fixed n ≥ 3, each of the Artin groups of finite type An, Bn = Cn, and affine type Ãn−1 and C̃n−1 is a central extension of a finite index subgroup of the mapping class group of the (n + 2)-punctured sphere. (The centre is trivial in the affine case and infinite cyclic in the finite type cases). Using results of Ivanov and Korkmaz on abstract commensurators of surface mapping...

Computation of fundamental groups of Galois covers recently led to the construction and analysis of Coxeter covers of the symmetric groups [RTV]. In this paper we consider analog covers of Artin’s braid groups, and completely describe the induced geometric extensions of the braid group.

We define a family of quasi-isometry invariants of groups called higher divergence functions, which measure isoperimetric properties “at infinity.” We give sharp upper and lower bounds on the divergence functions for right-angled Artin groups, using different pushing maps on the associated cube complexes. In the process, we define a class of RAAGs we call orthoplex groups, which have the proper...