@article {2007,
title = {Computing Amplitudes in topological M-theory},
number = {SISSA;74/2006/FM},
year = {2007},
abstract = {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. We show that when the target space is $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants.},
doi = {10.1088/1126-6708/2007/03/023},
url = {http://hdl.handle.net/1963/1901},
author = {Giulio Bonelli and Alessandro Tanzini and Maxim Zabzine}
}