Abstract

The Chern–Simons (CS) form started as a curious obstruction in mathematics 40 years ago, to become a central object in theoretical physics. CS terms are central features in high temperature superconductivity and in recently discovered topological insulators. In classical physics, the minimal coupling in electromagnetism and the action for a mechanical system in Hamiltonian form are examples of CS functionals. CS forms are also the natural generalization of the minimal coupling between the electromagnetic field and an even-dimensional membrane. Here, a cursory review of the role of CS forms in gravitation theories is presented at an introductory level.