From wall spaces to CAT(0) cube complexes
Geometric Topology
2007-05-23 v3 Group Theory
Abstract
We explain how to adapt a construction of M. Sageev's to construct a proper action on a CAT(0) cube complex starting from a proper action on a wall space, and use this to deduce that if G is a group containing an amenable subgroup H of super-polynomial growth and G acts properly on a space with walls then there are arbitrarily large families of walls in the wall space which pairwise cross.
Cite
@article{arxiv.math/0309036,
title = {From wall spaces to CAT(0) cube complexes},
author = {I. L. Chatterji and G. A. Niblo},
journal= {arXiv preprint arXiv:math/0309036},
year = {2007}
}
Comments
Updated to submitted version