  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, $k\geq 1$.
The key to extending the loop coproduct is the fact that the embedding
$M\rightarrow M^{S^{k-1}}$ is of "finite codimension" in a sense of Gorenstein
spaces. Moreover, we prove the associativity, commutativity, and Frobenius
compatibility of them.
