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: Blaom, Anthony D.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2022
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

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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last_indexed 2026-03-20T21:37:01Z
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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
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