Multiplicative Ehresmann connections

Rui Loja Fernandes, Ioan Mărcuţ

Research output: Contribution to journalArticlepeer-review


We develop the theory of multiplicative Ehresmann connections for Lie groupoid submersions covering the identity, as well as their infinitesimal counterparts. We construct obstructions to the existence of such connections, and we prove existence for several interesting classes of Lie groupoids and Lie algebroids, including all proper Lie groupoids. We show that many notions from the theory of principal bundle connections have analogues in this general setup, including connections 1-forms, curvature 2-forms, Bianchi identity, etc. In [19] we provide a non-trivial application of the results obtained here to construct local models in Poisson geometry and to obtain linearization results around Poisson submanifolds.

Original languageEnglish (US)
Article number109124
JournalAdvances in Mathematics
StatePublished - Aug 15 2023


  • Lie algebroids
  • Lie groupoids
  • Multiplicative connections

ASJC Scopus subject areas

  • General Mathematics


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