# Monodromy and faithful representability of Lie groupoids

## TL;DR

This paper introduces a monodromy group associated with topological groupoids and demonstrates its utility in determining the existence of faithful representations, establishing invariance under Morita equivalence.

## Contribution

It constructs a monodromy group for topological groupoids and shows its invariance under Morita equivalence, providing a new tool to analyze faithful representability.

## Key findings

- Monodromy groups are constructed for topological groupoids.
- Morita equivalent groupoids share the same monodromy groups.
- Monodromy groups can test for the absence of faithful representations.

## Abstract

For any topological groupoid G and any homomorphism from a locally compact Hausdorff topological group K to G, we construct an associated monodromy group. We prove that Morita equivalent topological groupoids have the same monodromy groups. We show how the monodromy groups can be used to test if a Lie groupoid lacks faithful representations.