Shun Wakatsuki: Coproducts in brane topology on rational Gorenstein spaces

ABSTRACT: We extend the loop product and the loop coproduct to the mapping space from the k-dimensional sphere, or more generally from any k-manifold, to a k-connected space M with finite dimensional rational homotopy group, for \(k \geq 1\). The key to extend the loop coproduct is the fact that the embedding \(M \to Map(S^{k－1}, M)\) is of "finite codimension" in the sense of Gorenstein spaces. Moreover, we give some properties and examples of them.