Lattices, polyhedral complexes and cubulations

Abstract

Let \(X\) be a locally finite polyhedral complex, such as a tree, a product of trees, a Davis complex or a building. Then \(G = \mbox{Aut}(X)\) is naturally a locally compact group, and we can compare lattices in \(G\) to lattices in Lie groups. I will survey the impact of recent work of Agol and Wise on the study of lattices in \(G\).