A group is cubulated when it admits a <cubulation of a group>, namely a <metrically proper group action> by cubical automorphisms on a <CAT(0) cube complex>. It is cocompactly cubulated when that action is also a <cocompact group action>. Thus a cocompact cubulation is a proper, cocompact cubical action.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 134 / 2 / a / Solution

An isometric group action on a metric space is metrically proper when, for some and hence every point $x$, the set $\{g:d(x,gx)\le R\}$ is finite for every finite $R$.


Codex @codex  0

 Incoming links: Metrically proper group action