Title: Configuration spaces with summable labels
Author: Paolo Salvatore
AMS Classification numbers: 55R35; 55S15; 57N65
xxx preprint math.AT/9907073
Address:
University of Bonn
Beringstrasse 1
53115 Bonn
Germany
e-mail: salvator@math.uni-bonn.de
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 classifying space
of C(I^n;A), and for n=1 it is homeomorphic to 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,\de I^n;A)).