Configuration spaces with summable labels
نویسنده
چکیده
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(In, ∂In;A) is an n-fold classifying space of C(In;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(In, ∂In;A)).
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تاریخ انتشار 1999