Actions of higher rank, irreducible lattices on $\CAT(0)$ cubical complexes

T. Tam Nguyen Phan

Let $\Gamma$ be an irreducible lattice of $\Q$-rank $\ge 2$ in a semisimple Lie group of noncompact type. We prove that any action of $\Gamma$ on a $\CAT(0)$ cubical complex has a global fi…