We study the contribution of topologically non-trivial sectors to the vacuum functional Z_m of a model of massive fermions in two dimensions. By using recent results on non-minimal correlation functions we can write Z_m as a kind of sector expansion. In this series, the contribution of each sector is given by integrals of minimal correlation functions evaluated in the massless theory. Finally we comment on the application of our result to the analysis of some special cases. In particular we briefly show that Coleman's equivalence between the massive Thirring and sine-Gordon models is not affected when topology is taken into account.