Recognizing mapping spaces
by David Blanc
Abstract: The mapping space map(A,B) - that is, the set of continuous functions between two topological spaces A and B, endowed with the compact-open topology - play a central role in modern homotopy theory. One classical question arising in their study is: when is a given space X of the form map(A,Y), for a fixed space A (at least up to homotopy).
Historically, this problem has been studied mainly for the case when A is a sphere. We shall discuss some recent developments for the general case, and show how the notion of a "mapping algebra" (over an enriched theory) can be used to address the realization question.
Joint work with Bernard Badzioch and Wojciech Dorabiala