Action Dimension of Lattices in Euclidean Buildings

Abstract

The action dimension of a group G is the minimal dimension of a contractible manifold that G acts on properly discontinuously. We show that if G acts properly and cocompactly on a thick Euclidean building, then the action dimension is bounded below by twice the dimension of the building. We also compute the action dimension of S-arithmetic groups over number fields, partially answering a question of Bestvina, Kapovich, and Kleiner.