Semistability of cubulated groups

Abstract

We prove that all cubulated groups are semistable at infinity. In doing so we prove two further results about cubulations of groups. The first of these states that any one-ended cubulated group has a cubulation for which all halfspaces are one-ended. The second states that any cubulated group has a cubulation for which all quarterspaces are deep -- analogous to the fact that passing to the essential core of a given cubulation ensures that all halfspaces are deep.

arXiv comment25 pages, 7 figures; v2: minor changes to the introduction; v3: minor changes following referee's comments, to appear in Mathematische Annalen