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arXiv · 0705.3386

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

Frédéric Haglund
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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.

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Frédéric Haglund. 2007-05-23. Isometries of CAT(0) cube complexes are semi-simple. https://arxiv.org/abs/0705.3386

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