  In this note we generalize a result by Alekseev and Strobl for the case of
$p$-branes. We show that there is a relation between anomalous free current
algebras and "isotropic" involutive subbundles of $T\oplus \wedge^p T^*$ with
the Vinogradov bracket, that is a generalization of the Courant bracket. As an
application of this construction we go through some interesting examples:
topological strings on symplectic manifolds, topological membrane on
$G_2$-manifolds and topological 3-brane on $Spin(7)$ manifolds. We show that
these peculiar topological theories are related to the physical (i.e.,
Nambu-Goto) brane theories in a specific way. These topological brane theories
are proposed as microscopic description of topological M/F-theories.
