Event № 2258

A mapping algebra is a space X of the form map(A, Y) for a fixed space A. If A is a sphere, then there are plenty of different approaches allowing to determine whether a space X is an (n-fold) loop space and to find Y. Unfortunately these methods do not admit generalizations for more general spaces than (wedges of) spheres. We argue that the generalized question of recognition of mapping spaces becomes a question on the representability of certain functor, up to homotopy. In this talk we will formulate and outline the proof of the analog of Freyd and Brown representability theorems, up to homotopy.

Joint work with David Blanc.