Special Cube Complexes
by
Daniel Wise
McGill
Coauthors: Frederic Haglund

We identify a class of "special" nonpositively curved cube complexes that are closely related to right-angled Artin groups. We give applications to subgroup separability and linearity, and to Coxeter groups. Some sample consequence of our theory include:

1) Every word-hyperbolic Coxeter group has separable quasiconvex subgroups.

2) Let G be the group given by the HNN extension <a,b,t | U^t=V >. Then G is a subgroup of SL_n(Z) unless U and V have conjugate powers.

3) For each f.p. group Q, there is a short exact sequence 1-> N -> G -> Q - > 1 where G < SL_n(Z) and N is f.g.

Date received: February 26, 2006