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Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry
Інший ID:
2010 Mathematics Subject Classification: 22E60; 22E65; 03F55; 18B25; 18B40
DOI:10.3842/SIGMA.2017.007
DOI:10.3842/SIGMA.2017.007
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
562
Завантажень:
319
Анотація:
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.
