%0 Journal Article
%T Configuration spaces with summable labels
%A Paolo Salvatore
%J Mathematics
%D 1999
%I arXiv
%X Let M be an n-manifold, and let A be a space with a partial sum behaving as an n-fold loop sum. We define the space C(M;A) of configurations in M with summable labels in A via operad theory. Some examples are symmetric products, labelled configuration spaces, and spaces of rational curves. We show that C(I^n,dI^n;A) is an n-fold delooping of C(I^n;A), and for n=1 it is the classifying space by Stasheff. If M is compact, parallelizable, and A is path connected, then C(M;A) is homotopic to the mapping space Map(M,C(I^n,dI^n;A)).
%U http://arxiv.org/abs/math/9907073v1