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arXiv · 2405.07692

Holography of Higher Codimension Submanifolds: Riemannian and Conformal

Samuel Blitz·Josef Šilhan
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Abstract

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 these same tools, we also investigate the formal solutions to extension problems off of an embedded submanifold.

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Samuel Blitz, Josef Šilhan. 2024-05-13. Holography of Higher Codimension Submanifolds: Riemannian and Conformal. https://doi.org/10.3842/sigma.2025.002

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