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From double Lie groupoids to local Lie 2-groupoids

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Abstract

We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger’s fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated local Lie 2-groupoid, which leads us to propose a definition of a symplectic 2-groupoid.

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Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, State College, PA, 16802, USA

    Rajan Amit Mehta

  2. Department of Mathematics, Washington University in Saint Louis, One Brookings Drive, Saint Louis, Missouri, 63130, USA

    Xiang Tang

Authors
  1. Rajan Amit Mehta
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  2. Xiang Tang
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Correspondence to Rajan Amit Mehta.

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Mehta, R.A., Tang, X. From double Lie groupoids to local Lie 2-groupoids. Bull Braz Math Soc, New Series 42, 651–681 (2011). https://doi.org/10.1007/s00574-011-0033-4

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  • DOI: https://doi.org/10.1007/s00574-011-0033-4

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