Cocompactly cubulated crystallographic groups

Details Cocompactly cubulated crystallographic groups Cocompactly cubulated crystallographic groups

2012-02-20

arxiv.org/abs/1202.4462v2

Mathematics

Group Theory

Part of the earlier proof of Theorem 4.1 contained an inaccuracy which is remedied in the current version

Scientific paper

We prove that the simplicial boundary of a CAT(0) cube complex admitting a proper, cocompact action by a virtually $\integers^n$ group is isomorphic to the hyperoctahedral triangulation of $S^{n-1}$, providing a class of groups $G$ for which the simplicial boundary of a $G$-cocompact cube complex depends only on $G$. We also use this result to show that the cocompactly cubulated crystallographic groups in dimension $n$ are precisely those that are \emph{hyperoctahedral}. We apply this result to answer a question of Wise on cocompactly cubulating virtually free abelian groups.

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