A Characterisation of Smooth Maps into a Homogeneous Space
We generalize Cartan's logarithmic derivative of a smooth map from a manifold into a Lie group to smooth maps into a homogeneous space = /, and determine the global monodromy obstruction to reconstructing such maps from infinitesimal data. The logarithmic derivative of the embedding of a subm...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2022 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211639 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Characterisation of Smooth Maps into a Homogeneous Space. Anthony D. Blaom. SIGMA 18 (2022), 029, 15 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862718783124144128 |
|---|---|
| author | Blaom, Anthony D. |
| author_facet | Blaom, Anthony D. |
| citation_txt | A Characterisation of Smooth Maps into a Homogeneous Space. Anthony D. Blaom. SIGMA 18 (2022), 029, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We generalize Cartan's logarithmic derivative of a smooth map from a manifold into a Lie group to smooth maps into a homogeneous space = /, and determine the global monodromy obstruction to reconstructing such maps from infinitesimal data. The logarithmic derivative of the embedding of a submanifold Σ ⊂ becomes an invariant of Σ under symmetries of the ''Klein geometry'' , whose analysis is taken up in [SIGMA 14 (2018), 062, 36 pages, arXiv:1703.03851].
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| first_indexed | 2026-03-20T21:37:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211639 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-20T21:37:01Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Blaom, Anthony D. 2026-01-07T13:43:16Z 2022 A Characterisation of Smooth Maps into a Homogeneous Space. Anthony D. Blaom. SIGMA 18 (2022), 029, 15 pages 1815-0659 2020 Mathematics Subject Classification: 53C99; 22A99; 53D17 arXiv:1702.02717 https://nasplib.isofts.kiev.ua/handle/123456789/211639 https://doi.org/10.3842/SIGMA.2022.029 We generalize Cartan's logarithmic derivative of a smooth map from a manifold into a Lie group to smooth maps into a homogeneous space = /, and determine the global monodromy obstruction to reconstructing such maps from infinitesimal data. The logarithmic derivative of the embedding of a submanifold Σ ⊂ becomes an invariant of Σ under symmetries of the ''Klein geometry'' , whose analysis is taken up in [SIGMA 14 (2018), 062, 36 pages, arXiv:1703.03851]. The author is indebted to a referee who contributed the direct proof of integrability in Section 2. This substantially simplified the proof of the existence theorem appearing in earlier manuscripts. We thank Yuri Vyatkin, Sean Curry, Andreas Čap, and Rui Fernandes for helpful discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Characterisation of Smooth Maps into a Homogeneous Space Article published earlier |
| spellingShingle | A Characterisation of Smooth Maps into a Homogeneous Space Blaom, Anthony D. |
| title | A Characterisation of Smooth Maps into a Homogeneous Space |
| title_full | A Characterisation of Smooth Maps into a Homogeneous Space |
| title_fullStr | A Characterisation of Smooth Maps into a Homogeneous Space |
| title_full_unstemmed | A Characterisation of Smooth Maps into a Homogeneous Space |
| title_short | A Characterisation of Smooth Maps into a Homogeneous Space |
| title_sort | characterisation of smooth maps into a homogeneous space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211639 |
| work_keys_str_mv | AT blaomanthonyd acharacterisationofsmoothmapsintoahomogeneousspace AT blaomanthonyd characterisationofsmoothmapsintoahomogeneousspace |