SOLVING TOPOLOGICAL FIELD-THEORIES ON MAPPING TORI

Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1/1) m odel of Rozansky and Saleur on Sigma x S-1, both directly and using eq uivalent two-dimensional theories, We also derive the partition functi on of a certain non-abelian generalization of the U(1/1) model on mapp ing tori and hence obtain explicit expressions for the Ray-Singer tors ion on these manifolds, Extensions of these results to BF and Chem-Sim ons theories on mapping tori are also discussed. The topological field theory actions of the equivalent two-dimensional theories we find hav e the interesting property of depending explicitly on the diffeomorphi sm defining the mapping torus while the quantum field theory is sensit ive only to its isomorphism class defining the mapping torus as a smoo th manifold.