A Chern-Simons form is an odd-degree transgression form whose exterior derivative is an invariant polynomial in the curvature form. For the trace polynomial of degree , ; the Chern-Simons 3-form is the degree-three case.
The Chern–Simons form is a mathematical construct that arises in differential geometry and theoretical physics, particularly in the study of gauge theories and topology. It is named after the mathematicians Shiing-Shen Chern and James Simons. In essence, the Chern–Simons form is a differential form associated with a connection on a principal bundle, and it helps in the definition of topological invariants of manifolds, notably in the context of 3-manifolds.
New to topics? Read the docs here!