We present a topological quantum field theory which corresponds to the moduli problem associated to Witten’s monopole equations for four-manifolds. The construction of the theory is carried out in purely geometrical terms using the Mathai-Quillen formalism, and the corresponding observables are described. These provide a rich set of new topological quantites. ⋆ E-mail: [email protected] In ...

An action principle is described which unifies general relativity and topological field theory. An additional degree of freedom is introduced, and depending on the value it takes the theory has solutions that reduce it to 1) general relativity in Palatini form, 2) general relativity in the Ashtekar form, 3) F ∧ F theory for SO(5) and 4) BF theory for SO(5). This theory then makes it possible to...