  We extend the structure of string topology from mapping spaces to embedding
spaces $Emb(S^n,M)$. This extension comes from an action of the cleavage
operad, a coloured $E_{n+1}$-operad. For all values of $n \in \mathbb{N}$, this
gives an action of certain Thom spectra that provides an action on the level
homology. We provide an analysis of the string topology structure derived from
the embedding $Emb(S^n,M) \hookrightarrow Map(S^n,M)$. In the $1$-dimensional
case it specializes a morphism of BV-algebras $\mathbb{H}_*(Emb(S^1,M)) \to
\mathbb{H}_*(Map(S^1,M)$.
