The formulation of the Chern-Simons action for general compact Lie groups using Deligne cohomology (Q2757135)

We formulate the Chern-Simons action for any compact Lie group using Deligne cohomology. This action is defined as a certain function on the space of smooth maps from the underlying 3-manifold to the classifying space for principal bundles. If the 3-manifold is closed, the action is a \({\mathbb{C}}^*\)-valued function. If the 3-manifold is not closed, then the action is a section of a hermitian line bundle associated with the Riemann surface which appears as the boundary.