The paper continues a series of earlier works that showed a deep relationship between Poincare supersymmetry and topological symmetry. It discusses the quantization of a holomorphic 2-form coupled to a Yang-Mills field on special manifolds in various dimensions. These theories are basically “almost topological quantum field theories” in the sense that their observables are invariant under restricted changes of the metric, the prototype being the holomorphic BF action, whose quantization requires the Batalin-Vilkovisky formalism and admits a “twist” operation, i.e. a mapping from the ghost and antighost fermionic degrees of freedom onto spinors entailing \(N=1\) supersymmetry. For Kähler manifolds in four dimensions this topological model is related to \(N=1\) super Yang-Mills theory. Extended supersymmetries are recovered by considering the coupling with chiral multiplets. Other examples are provided by Calabi-Yau three- and fourfolds and 7-dimensional \(G_2\) manifolds of the kind discussed by N. Hitchin [“Stable forms and special metrics”, in Proceedings of the Congress in memory of Alfred Gray (AMS Contemporary Mathematics Series)]. The authors argue that the 2-form field could play an interesting role in the study of the conjectured S-duality in topological strings. Finally they show that in the case of real forms the partition function of their topological model in 6 dimensions is related to the square of that of the holomorphic Chern-Simons theory, and they discuss its lift to 7 dimensions and its relation to the conjectured topological M-theory.