Primary Meridian Obstructions Under Admissible Reconstruction: A Local-to-Global Topological Framework for Codimension, Holonomy, and Persistence
Bin Li · International Journal of Topology · 2026
This paper organizes classical tools from complement topology into a local-to-global framework for primary meridian obstructions under admissible reconstruction. Let D⊂Md be a closed properly embedded submanifold of pure codimension c, and put X=M∖D. With coefficients for which the normal bundle is oriented, excision and the Thom isomorphism identify a relative fiber class τa∈Hc(M,X) for each component Da⊂D. The connecting morphism sends this class to the global meridian μa=∂τa∈Hc−1(X). Thus, the familiar sphere or loop in a local normal slice survives globally precisely when τa is not supplied by an ambient c-cycle. Nonvanishing implies that the normal linking sphere is not null-homotopic and gives the primary degree–codimension relation k=c−1. Basepoint, orientation, disconnected-support, and nonorientable-normal-bundle issues are treated explicitly. A fixed-resolution tubular filling shows how a meridian can be killed when restoration of the defect center is admissible; under uniform tubular geometry, its support is controlled by the (d−c)-volume of the affected support. In codimension two, the surviving class lies in H1(X), the abelianization of the fundamental group, and is therefore the topological input available to a homotopy-invariant U(1) phase read-out. Compatible characters retain their meridian value under admissible continuation maps. The aim is not to introduce a new complement invariant or general classification theorem, but to provide a rigorous, reusable synthesis that keeps local detection, global survival, character evaluation, and continuation hypotheses logically distinct.