## The Formulation of the Chern-Simons Action for General Compact Lie Groups Using Deligne Cohomology

J. Math. Sci. Univ. Tokyo
Vol. 8 (2001), No. 2, Page 223--242.

Gomi, Kiyonori
The Formulation of the Chern-Simons Action for General Compact Lie Groups Using Deligne Cohomology
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 ${\bf C}^*$-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.