be extended and defined in the interior, then The Frobenius consistency condition now becomes As the previous equation is valid for any arbitrary extension of the fields into the interior, Because of the Frobenius consistency condition, this means that there exists a d+1-form Ω(d+1) (not depending upon ε) defined over Md+1 satisfying Ω(d+1) is often called a Chern–Simons form. Once again, if we assume Ω(d+1) can be expressed as an exterior product and that it can be extended into a d+1 -form in a d+2 dimensional oriented manifold, we can define in d+2 dimensions. Ω(d+2) is gauge invariant: as d and δε commute. See also Chiral gauge theory Anomaly matching condition Green–Schwarz mechanism Mixed anomaly References Anomalies (physics)