2026/07/23 by Roger Bergadà Batlles
Mathematics · #math.AT
A simple complex of groups is a functor from a poset to the category of groups satisfying certain properties. They were introduced by Bridson and Haefliger as an abstract way to encode isotropy subgroups of actions on posets. A simplex complex of groups which embeds in a group K has an associated K-poset. We will explain how to obtain information about the classifying space of K through the K-equivariant homotopy type of the construction of Bridson-Haefliger, and we will also obtain finiteness properties of cohomology.