Isometries of CAT(0) cube complexes are semi-simple
Group Theory
2007-05-24 v1
Abstract
We show that an automorphism of an arbitrary CAT(0) cube complex either has a fixed point or preserves some combinatorial axis. It follows that when a group contains a distorted cyclic subgroup, it admits no proper action on a discrete space with walls.
Keywords
Cite
@article{arxiv.0705.3386,
title = {Isometries of CAT(0) cube complexes are semi-simple},
author = {Frédéric Haglund},
journal= {arXiv preprint arXiv:0705.3386},
year = {2007}
}