Holography of Higher Codimension Submanifolds: Riemannian and Conformal - Blitz, Samuel; Šilhan, Josef (Symmetry, Integrability and Geometry: Methods and Applications, 2025)
We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of which depend on a choice of parallelization of the normal bundle. Qualitatively new behavior is observed in the higher-codimension case, giving rise to new invariants that obstruct the order-by-order construction of unit-defining maps. In the conformal setting, a novel invariant (that vanishes in codimension 1) is realized as the leading transverse-order term appearing in a holographically-constructed Willmore invariant. Using the same tools, we also investigate formal solutions to extension problems off an embedded submanifold.