Relative Center Class

Meaning

The relative center class records the failure of a marked external center source to admit an ordinary admissible filling.

For a meridional cocycle in center sector , the paper defines

The homotopy fiber is doing real work. Its two coordinates distinguish a refinement representative from the admissible correction needed to compare that representative with ordinary filling data. The zero in the first coordinate says that no new bulk refinement class is being inserted. The second coordinate records the collar datum that ordinary admissibility would have to absorb.

So means more than “the source has a center character.” It says that the marked source datum cannot be erased merely by changing the admissible filling representative.

Example (illustrative)

Walk once around a collar meridian linking an external source. If the normalized cocycle evaluates to , an ordinary admissible filling would have to remove that nonzero evaluation. The relative class records that this removal is unavailable inside the declared filling complex.

Scope and limits

The class labels a topological obstruction. It does not itself provide a positive operator, a frame inequality, an energy density, or a string. Those require later represented analytic constructions.

Source

Phenomenological Implications I, §3.1, Definition 3.1 and Proposition 3.2.

Read the source manuscript.