nLab
Lie theory for stacky Lie groupoids

Context

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Contents

Definition: Stacky Lie groupoid

A stacky Lie groupoid (in contrast to a Lie groupoid) is an internal groupoid in the category of differentiable stacks, such that the space of objects is an ordinary manifold.

Notice that differentiable stacks are equivalent to Lie groupoids modulo Morita equivalence.

Literature

Stacky Lie groupoids and their Lie theory were introduced and studied by Chenchang Zhu and collaborators.

  • Chenchang Zhu, n-Groupoids and Stacky Groupoids, 2008, International Mathematics Research Notices (2009) 2009:4087-4141; (http://arxiv.org/abs/0801.2057 arXiv:0801.2057). DOI: (http://dx.doi.org/10.1093/imrn/rnp080 10.1093/imrn/rnp080).

  • C.Z., Lie nn-groupoids and stacky Lie groupoids (arXiv)

  • C. Z., Lie II theorem for Lie algebroids via stacky Lie groupoids (arXiv)

  • C. Z. Lie II theorem (pdf slides)

  • Henrique Bursztyn, C.Z., Morita equivalence of Poisson manifold via stack groupoids (arXiv)

Further resources

  • nn-Café blog discussion about this is here.
Revised on November 10, 2016 23:22:14 by David Roberts (129.127.37.77)