  Given smooth manifolds $M$ and $N$, manifold calculus studies the space of
embeddings $\operatorname{Emb}(M,N)$ via the "embedding tower", which is
constructed using the homotopy theory of presheaves on $M$. The same theory
allows us to study the stable homotopy type of $\operatorname{Emb}(M,N)$ via
the "stable embedding tower". By analyzing cubes of framed configuration
spaces, we prove that the layers of the stable embedding tower are tangential
homotopy invariants of $N$.
  If $M$ is framed, the moduli space of disks $E_M$ is intimately connected to
both the stable and unstable embedding towers through the $E_n$ operad. The
action of $E_n$ on $E_M$ induces an action of the Poisson operad
$\mathrm{pois}_n$ on the homology of configuration spaces $H_*(F(M,-))$.
  In order to study this action, we introduce the notion of Poincare-Koszul
operads and modules and show that $E_n$ and $E_M$ are examples. As an
application, we compute the induced action of the Lie operad on $H_*(F(M,-))$
and show it is a homotopy invariant of $M^+$.
