The Euler characteristic of configuration spaces (Q6050048)

This paper discusses the Euler characteristic of the ordered configuration spaces \(F(X,n)\) of \(n\) distinct points on a topological space \(X\). The exponential generating function for the Euler characteristic of \(F(X,n)\) is known in the case of a manifold \(X=M\) and \(X\) a finite simplicial complex. For the compactly supported Euler characteristic it is also known if \(X\) is a locally compact Hausdorff space. Those results are generalized to the compactly supported case and \(X=\bigcup_\alpha X_\alpha\) a topologically stratified space of finite type.