The Euler characteristic of configuration spaces

Abstract

In this short note we present a generating function computing the compactly supported Euler characteristic ${\chi }_c(F(X,n),K^{⊠n})$ of the configuration spaces on a topologically stratified space $X$, with $K$ a constructible complex of sheaves on $X$, and we obtain as a special case a generating function for the Euler characteristic $\chi (F(X,n))$. We also recall how to use existing results to turn our computation of the Euler characteristic into a computation of the equivariant Euler characteristic.

9 pages, minor changes from the previous version, most importantly to better adress the similarity and differences with another result already published by Baryshnikov

References in corpus (1)

• Mixed Hodge structures of configuration spaces