# Superrigidity of actions on finite rank median spaces

@article{Fioravanti2017SuperrigidityOA,
title={Superrigidity of actions on finite rank median spaces},
author={Elia Fioravanti},
journal={arXiv: Geometric Topology},
year={2017}
}
Finite rank median spaces are a simultaneous generalisation of finite dimensional CAT(0) cube complexes and real trees. If $\Gamma$ is an irreducible lattice in a product of rank one simple Lie groups, we show that every action of $\Gamma$ on a complete, finite rank median space has a global fixed point. This is in sharp contrast with the behaviour of actions on infinite rank median spaces. The fixed point property is obtained as corollary to a superrigidity result; the latter holds for… Expand
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