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

math.GT

/ Authors

/ Abstract

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

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

math.GT

/ Authors

T. Tam Nguyen Phan

/ Abstract

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