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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2017 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2017
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148557 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862545051407613952 |
|---|---|
| author | Burke, M. |
| author_facet | Burke, M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-25T04:41:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148557 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T04:41:28Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Burke, M. 2019-02-18T15:39:03Z 2019-02-18T15:39:03Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/148557 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. The author is very grateful for the constructive comments of fered by and the important corrections
 indicated by the editor and referees. The author would like to acknowledge the assistance
 of Richard Garner, my Ph.D. supervisor at Macquarie University Sydney, who provided valuable
 comments and insightful discussions in the genesis of this work. In addition the author is grateful
 for the support of an International Macquarie University Research Excellence Scholarship. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry Article published earlier |
| spellingShingle | Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry Burke, M. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148557 |
| work_keys_str_mv | AT burkem connectedliegroupoidsareinternallyconnectedandintegralcompleteinsyntheticdifferentialgeometry |