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On the existence of global bisections of Lie groupoids

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Abstract

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.

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Authors and Affiliations

  1. Center of Mathematics, China Youth University for Political Sciences, Beijing, 100089, P. R. China

    De Shou Zhong

  2. Department of Mathematics and LMAM, Peking University, Beijing, 100871, P. R. China

    Zhuo Chen & Zhang Ju Liu

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  1. De Shou Zhong
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  2. Zhuo Chen
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  3. Zhang Ju Liu
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Correspondence to De Shou Zhong.

Additional information

Supported by NSFC (Grant No. 10871007) and CPSF (Grant No. 20060400017)

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Zhong, D.S., Chen, Z. & Liu, Z.J. On the existence of global bisections of Lie groupoids. Acta. Math. Sin.-English Ser. 25, 1001–1014 (2009). https://doi.org/10.1007/s10114-009-6242-8

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  • DOI: https://doi.org/10.1007/s10114-009-6242-8

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