  We study the quantization of a holomorphic two-form coupled to a Yang-Mills
field on special manifolds in various dimensions, and we show that it yields
twisted supersymmetric theories. The construction determines ATQFT's (Almost
Topological Quantum Field Theories), that is, theories with observables that
are invariant under changes of metrics belonging to restricted classes. For
Kahler manifolds in four dimensions, our topological model is related to N=1
Super Yang-Mills theory. Extended supersymmetries are recovered by considering
the coupling with chiral multiplets. We also analyse Calabi-Yau manifolds in
six and eight dimensions, and seven dimensional G_2 manifolds of the kind
recently discussed by Hitchin. We argue that the two-form field could play an
interesting role for the study of the conjectured S-duality in topological
string. We finally show that in the case of real forms in six dimensions the
partition function of our topological model is related to the square of that of
the holomorphic Chern-Simons theory, and we discuss the uplift to seven
dimensions and its relation with the recent proposals for the topological
M-theory.
