Discrete Configuration Spaces of Generalized Simplicial Complexes

5 Discrete Configuration Spaces of Generalized Simplicial Complexes 

A standard concept in algebraic topology is that of a configuration space. Here we consider the discrete version. 

A special case of DCn A), when A is 1-dimensional, has been a subject of extensive recent study. In this case the complex is actually cubical, a fact that can be used to advantage in applying the methods of geometric group theory. 

We can connect the discrete configuration spaces to Horn complexes by noticing that for any generalized simphcial complex A and any positive integer n, we have 

The identity (9.2) motivates the introduction of the following more general 

---