Proper Cartan Groupoids: Reduction to the Regular Case

TL;DR

This paper presents a method to simplify the construction of multiplicative connections on proper Lie groupoids by reducing the problem to cases involving proper and regular Lie groupoids, making the task more manageable.

Contribution

It introduces a reduction technique that transforms the problem of constructing multiplicative connections on proper Lie groupoids into simpler subproblems involving proper and regular groupoids.

Findings

Reduction method simplifies constructing multiplicative connections.

Applicable to proper Lie groupoids, focusing on regular cases.

Facilitates easier analysis and construction of connections.

Abstract

We discuss a method for constructing multiplicative connections on proper Lie groupoids or, more exactly, for reducing the task of constructing such connections to a number of in principle simpler tasks involving only Lie groupoids that are both proper and regular.