English

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}
}