example one can take the action $$S[\omega]=i\int_{M}\omega_{n}d\omega_{n},\qquad \dim M=2n+1\no$$ where $\omega_n$ is an $n$-form. The partition function is then $$Z[M]=\int {\cal D}\omega\mu[\omega]\exp[S[\omega]] \no$$ $S[\omega] $ has a gauge invariance whereby $S[\omega]=S[\omega+d\lambda]$ and therefore to define the partition function it is necessary to integrate over only inequivalent field configurations. The measure ${\cal D}\omega\mu[\omega]$ thus contains functional delta functions which constrain the integration and play the role of gauge fixing, together with their associated determinants. This measure can be constructed using, for example, the Batalin-Vilkovisky BRST construction \[11,12\].

We shall be concerned here with the special situation of three dimensions and with the case where the three manifold $M$ is a lens space. The topological field theory of interest to us in this paper is given by the action $$S[\omega]=i\int_{M}\omega_1 d\omega_1 \no$$ where $\omega_1$ is now a $1$-form. To construct the integration measure we will follow the Batalin-Vilkovisky BRST construction \[11,12\]. The essential element of this construction is what is termed a gauge Fermion” whose BRST variation gives the gauge fixing and ghost portion of the BRST invariant action. Integrating out these fields yields the contribution $\mu[\omega]$ to the measure.

The gauge Fermion is constructed by choosing a gauge fixing for the 