Coproducts in brane topology

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 with finite-dimensional rational homotopy group for $k\ge 1$. The key to extending the loop coproduct is the fact that the embedding $M\to M^{S^{k-1}}$ is of “finite codimension” in the sense of Gorenstein spaces. Moreover, we prove the associativity, commutativity and Frobenius compatibility of them.