Giorgio Trentinaglia
Published 2014-03-09, updated 2015-05-19Version 2
Motivated by the study of global geometric properties of differentiable stacks presented by proper Lie groupoids, we investigate the existence of multiplicative connections on such groupoids. We show that one can always deform a given connection which is only approximately multiplicative into a genuinely multiplicative connection. The proof of this fact presented here relies on a recursive averaging technique. We regard our results as a preliminary step towards the construction of an obstruction theory for multiplicative connections on proper Lie groupoids.
Comments: 60 pages. In the new version, more general statements of the main theorems are given which do no longer rely on the assumption of source-properness. As a consequence, Appendix B has been expanded. Some minor changes have been introduced throughout, especially to the terminology. The introduction has been rewritten. Some references have been added
On the linearization theorem for proper Lie groupoids
Fast convergence techniques in the study of Lie groupoid representations
Riemannian metrics on Lie groupoids
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