BRST quantization of topological field theory

The canonical quantization of the topological field-theory model $\int M^{}F\wedge B$, proposed by Horowitz, is examined through the Becchi-Rouet-Stora-Tyutin approach. With this approach we have a manifestly covariant description of a certain class of topological quantum field theories. However, if $M$ in the present model is any orientable four-dimensional manifold, one would end up with different theories when different polarizations are chosen. Therefore a restriction $M=R^1\times \Sigma$, as pointed out by Horowitz, is required for consistency.