  We consider a deformation of the BF theory in any dimension by means of the
antifield BRST formalism. Possible consistent interaction terms for the action
and the gauge symmetries are analyzed and we find a new class of topological
gauge theories. Deformations of the world volume BF theory are considered as
possible deformations of the topological open membrane. Therefore if we
consider these theories on open membranes, we obtain noncommutative structures
of the boundaries of open membranes, and we propose a generalization of the
path integral representation of the star deformation.
