  Given a smooth oriented manifold $M$ with non-empty boundary, we study the
Pontryagin algebra $A=H_\ast(\Omega )$ where $ \Omega $ is the space of loops
in $M$ based at a distinguished point of $ \partial M$. Using the ideas of
string topology of Chas-Sullivan, we define a linear map $\{\{-,-\}\}: A
\otimes A \to A\otimes A$ which is a double bracket in the sense of Van den
Bergh satisfying a version of the Jacobi identity. For $\dim(M)\geq 3$, the
double bracket $\{\{-,-\}\}$ induces Gerstenhaber brackets in the
representation algebras associated with $A$. This extends our previous work on
the case $\dim(M)=2$ where $A= H_0(\Omega )$ is the group algebra of the
fundamental group $\pi_1(M)$ and the double bracket $\{\{-,-\}\}$ induces the
standard Poisson brackets on the moduli spaces of representations of
$\pi_1(M)$.
