International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 23, Pages 1465-1480

Universal connections on Lie groupoids

Efstathios Vassiliou and Apostolos Nikolopoulos

Department of Mathematics, University of Athens, Panepistimiopolis, Athens 15784, Greece

Received 7 November 2001

Copyright © 2003 Efstathios Vassiliou and Apostolos Nikolopoulos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Given a Lie groupoid Ω, we construct a groupoid J1Ω equipped with a universal connection from which all the connections of Ω are obtained by certain pullbacks. We show that this general construction leads to universal connections on principal bundles (considered by García (1972)) and universal linear connections on vector bundles (ultimately related with those of Cordero et al. (1989)).