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

Abstract

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 fixed point.

5 pages, 1 figure. arXiv admin note: text overlap with arXiv:1108.4127