ABSTRACT
A field theory is topological if the partition function and the correlation functions do not depend on a choice of metric on a manifold. Reidemeister torsion arises naturally in the formulas for the stationary phase approximation to Chern-Simons gauge theory. An alternative version of the Duistermaat-Heckman theorem asserts that the push-forward of the symplectic or Liouville measure by the moment map for a torus action is a piecewise polynomial function. The moduli spaces have a symplectic structure which generalizes the symplectic structure on the Jacobian. More generally the residue is specified by certain axioms, and may be defined as a sum of iterated multivariable residues for a suitably chosen basis of yielding coordinates. Victor Guillemin and J. Kalkman and independently S.K. Martin have given an alternative version of the residue formula which uses the one-variable proof inductively. Witten’s derivation of the formulas amounts to an infinite dimensional version of non-Abelian localization.
