Isometries of $CAT(0)$ cube complexes are semi-simple

Frédéric Haglund (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: $CAT(0)$ Cube Complexes; Spaces with walls; Baumslag-Solitar Groups

Domaines: Théorie des groupes [math.GR]

Frédéric Haglund. Isometries of $CAT(0)$ cube complexes are semi-simple. 2007. ⟨hal-00148515⟩