COMMENSURATORS OF RIGHT-ANGLED ARTIN GROUPS AND MAPPING CLASS GROUPS MATT CLAY, CHRISTOPHER J. LEININGER, AND DAN MARGALIT Abstract. We prove that, aside from the obvious exceptions, the mapping class We prove that, aside from the obvious exceptions, the mapping class group of a compact orientable surface is not abstractly commensurable with any right-angled Artin group. Our argument applies to...

Tree lattices have been well-studied (see [BL]). Less understood are lattices on higherdimensional CAT(0) complexes. In this paper, we consider lattices on X a locally finite, regular right-angled building (see Davis [D] and Section 1 below). Examples of such X include products of locally finite regular or biregular trees, or Bourdon’s building Ip,q [B], which has apartments hyperbolic planes t...

We study Kazhdan-Lusztig cells and corresponding representations of right-angled Coxeter groups and Hecke algebras associated with them. In case of the infinite groups generated by reflections of hyperbolic plane in the sides of right-angled polygons we obtain a complete explicit description of the left and two-sided cells. In particular, it appears that there are infinitely many left cells but...

We establish sufficient conditions implying semistability and connectivity at infinity properties for CAT(0) cubical complexes. We use this, along with the geometry of cubical K(π, 1)’s to give a complete description of the higher connectivity at infinity properties of right angled Artin groups. Among other things, this determines which right angled Artin groups are duality groups. Applications...

A new method for combining small-sized areal array CCD sensors to make one wide-angled digital aerial photography system is studied in this paper. The method is to install several small-sized areal array CCD cameras in the way that their perspective projecting centers form a line or a square, with their principal optical axes slanting fixed angle along designed directions. Such installation aim...

We develop an analogy between right-angled Artin groups and mapping class groups through the geometry of their actions on the extension graph and the curve graph respectively. The central result in this paper is the fact that each right-angled Artin group acts acylindrically on its extension graph. From this result we are able to develop a Nielsen–Thurston classification for elements in the rig...

We associate to each right-angled Coxeter group a 2-dimensional complex. Using this complex, we show that if the presentation graph of the group is planar, then the group has a subgroup of finite index which is a 3-manifold group (that is, the group is virtually a 3-manifold group). We also give an example of a right-angled Coxeter group which is not virtually a 3-manifold group.

Let (W,S) be a Coxeter system and let s ∈ S. We call s a right-angled generator of (W,S) if st = ts or st has infinite order for each t ∈ S. We call s an intrinsic reflection of W if s ∈ RW for all Coxeter generating sets R of W . We give necessary and sufficient conditions for a right-angled generator s ∈ S of (W,S) to be an intrinsic reflection of W .