A combination theorem for special cube complexes

作者：Haglund Frederic^*; Wise Daniel T

来源：Annals of Mathematics, 2012, 176(3): 1427-1482.

DOI：10.4007/annals.2012.176.3.2

We prove that certain compact cube complexes have special finite covers. This means they have finite covers whose fundamental groups are quasiconvex sub-groups of right-angled Artin groups. As a result we obtain, linearity and the separability of quasiconvex subgroups, for the groups we consider. Our result applies in particular to compact negatively curved cube complexes whose hyperplanes don't self-intersect. For cube complexes with word-hyperbolic fundamental group, we are able to show that they are virtually special if and only if the hyperplanes are separable. In a final application, we show that the fundamental groups of every simple type uniform arithmetic hyperbolic manifolds are cubical and virtually special.

• 出版日期2012-11