It is remarkable that for any ordered set of variables {t,x,y,z,....}, the 1form of Action, A = At * dt + Ax*dx + ..., will generate a 2form F, and if the functions are C2, then dF = 0, for any dimension N. No matter how large N is, the first four equations of dF= 0 are exactly of the same format as the Maxwell  Faraday equations of electromagnetic theory. No new variables beyond the E and B six components appear in the first 4 equations of dF = 0.
The Maxwell  Faraday equations form a nested set. The fifth and sequentially
other equations of dF = 0 do link the higher dimensional components to those
classically recognized as the electromagnetic E and B fields. However, no new
terms appear in the first four equations!
This result is strong evidence for the topological basis of electromagnetic
theory.
