On the existence of global bisections of Lie groupoids

被引：0

作者：

De Shou Zhong

Zhuo Chen

Zhang Ju Liu

机构：

[1] China Youth University for Political Sciences,Center of Mathematics

[2] Peking University,Department of Mathematics and LMAM

来源：

Acta Mathematica Sinica, English Series | 2009年 / 25卷

关键词：

Lie groupoid; bisection; exponential map; 17B62; 17B70;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We show that every source connected Lie groupoid always has global bisections through any given point. This bisection can be chosen to be the multiplication of some exponentials as close as possible to a prescribed curve. The existence of bisections through more than one prescribed point is also discussed. We give some interesting applications of these results.

引用

页码：1001 / 1014

页数：13

共 10 条

[1]

Ehresmann C.(1957)Gattungen von lokalen Strukturen Jber. Deutsch. Math. Verein. 60 49-77

[2]

Ehresmann C.(1983)Œuvres complètes et commentées. I-1,2. Topologie algébrique et géométrie différentielle Cahiers Topologie Géom. Différentielle 24 1-A910

[3]

Pradines J.(1966)Théorie de Lie pour les groupoïdes différentiables. Relations entre propriétés locales et globales C. R. Acad. Sci. Paris Sér. A-B 263 A907-A248

[4]

Pradines J.(1967)Théorie de Lie pour les groupoï des différentiables. Calcul différenetiel dans la catégorie des groupoï des infinitésimaux C. R. Acad. Sci. Paris Sér. A-B 264 A245-104

[5]

Weinstein A.(1987)Symplectic groupoids and Poisson manifolds Bull. Amer. Math. Soc. (N. S.) 16 101-727

[6]

Weinstein A.(1988)Coisotropic calculus and Poisson groupoids J. Math. Soc. Japan 40 705-234

[7]

Karasëv M. V.(1989)The Maslov quantization conditions in higher cohomology and analogs of notions developed in Lie theory for canonical fibre bundles of symplectic manifolds. I, II Selecta Math. Soviet. 8 213-395

[8]

Zakrzewski S.(1990)Quantum and classical pseudogroups. II. Differential and symplectic pseudogroups Comm. Math. Phys. 134 371-756

[9]

Zhong D. S.(2003)On the action of a groupoid on a manifold Acta Mathematica Sinica, English Series 19 745-undefined

[10]

He L. G.(undefined)undefined undefined undefined undefined-undefined

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