We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. ...

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 ...

We construct a gauge fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this ...