Holography of Higher Codimension Submanifolds: Riemannian and Conformal
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-codi...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2025 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2025
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212889 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Holography of Higher Codimension Submanifolds: Riemannian and Conformal. Samuel Blitz and Josef Šilhan. SIGMA 21 (2025), 002, 41 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862623149787447296 |
|---|---|
| author | Blitz, Samuel Šilhan, Josef |
| author_facet | Blitz, Samuel Šilhan, Josef |
| citation_txt | Holography of Higher Codimension Submanifolds: Riemannian and Conformal. Samuel Blitz and Josef Šilhan. SIGMA 21 (2025), 002, 41 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2026-03-21T11:57:02Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212889 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:57:02Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Blitz, Samuel Šilhan, Josef 2026-02-13T13:51:20Z 2025 Holography of Higher Codimension Submanifolds: Riemannian and Conformal. Samuel Blitz and Josef Šilhan. SIGMA 21 (2025), 002, 41 pages 1815-0659 2020 Mathematics Subject Classification: 53C18; 53A55; 53C21; 58J32 arXiv:2405.07692 https://nasplib.isofts.kiev.ua/handle/123456789/212889 https://doi.org/10.3842/SIGMA.2025.002 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. SB and JŠ are supported by the Czech Science Foundation (GACR) grant GA22-00091S. SB is also supported by the Operational Programme Research, Development and Education Project No. CZ.02.01.01/00/22-010/0007541. SB and JŠ would like to thank A. Rod Gover and Andrew Waldron for helpful comments and insights, and the anonymous referees for relevant contributions to improve this work. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Holography of Higher Codimension Submanifolds: Riemannian and Conformal Article published earlier |
| spellingShingle | Holography of Higher Codimension Submanifolds: Riemannian and Conformal Blitz, Samuel Šilhan, Josef |
| title | Holography of Higher Codimension Submanifolds: Riemannian and Conformal |
| title_full | Holography of Higher Codimension Submanifolds: Riemannian and Conformal |
| title_fullStr | Holography of Higher Codimension Submanifolds: Riemannian and Conformal |
| title_full_unstemmed | Holography of Higher Codimension Submanifolds: Riemannian and Conformal |
| title_short | Holography of Higher Codimension Submanifolds: Riemannian and Conformal |
| title_sort | holography of higher codimension submanifolds: riemannian and conformal |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212889 |
| work_keys_str_mv | AT blitzsamuel holographyofhighercodimensionsubmanifoldsriemannianandconformal AT silhanjosef holographyofhighercodimensionsubmanifoldsriemannianandconformal |