Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry
We extend some fundamental definitions and constructions in the established generalisation of Lie theory involving Lie groupoids by reformulating them in terms of groupoids internal to a well-adapted model of synthetic differential geometry. In particular we define internal counterparts of the defin...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2017 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148557 |
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| Цитувати: | Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry / M. Burke // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 27 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148557 |
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irk-123456789-1485572019-02-19T01:25:56Z Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry Burke, M. We extend some fundamental definitions and constructions in the established generalisation of Lie theory involving Lie groupoids by reformulating them in terms of groupoids internal to a well-adapted model of synthetic differential geometry. In particular we define internal counterparts of the definitions of source path and source simply connected groupoid and the integration of A-paths. The main results of this paper show that if a classical Hausdorff Lie groupoid satisfies one of the classical connectedness conditions it also satisfies its internal counterpart. 2017 Article Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry / M. Burke // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 22E60; 22E65; 03F55; 18B25; 18B40 DOI:10.3842/SIGMA.2017.007 http://dspace.nbuv.gov.ua/handle/123456789/148557 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We extend some fundamental definitions and constructions in the established generalisation of Lie theory involving Lie groupoids by reformulating them in terms of groupoids internal to a well-adapted model of synthetic differential geometry. In particular we define internal counterparts of the definitions of source path and source simply connected groupoid and the integration of A-paths. The main results of this paper show that if a classical Hausdorff Lie groupoid satisfies one of the classical connectedness conditions it also satisfies its internal counterpart. |
| format |
Article |
| author |
Burke, M. |
| spellingShingle |
Burke, M. Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Burke, M. |
| author_sort |
Burke, M. |
| title |
Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry |
| title_short |
Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry |
| title_full |
Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry |
| title_fullStr |
Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry |
| title_full_unstemmed |
Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry |
| title_sort |
connected lie groupoids are internally connected and integral complete in synthetic differential geometry |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148557 |
| citation_txt |
Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry / M. Burke // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 27 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT burkem connectedliegroupoidsareinternallyconnectedandintegralcompleteinsyntheticdifferentialgeometry |
| first_indexed |
2023-05-20T17:29:44Z |
| last_indexed |
2023-05-20T17:29:44Z |
| _version_ |
1796153422686191616 |