# Principal bundle groupoids, their gauge group and their nerve

@inproceedings{Garmendia2021PrincipalBG, title={Principal bundle groupoids, their gauge group and their nerve}, author={Alfonso Garmendia and Sylvie Paycha}, year={2021} }

We consider groupoids in the category of principal bundles, which we call principal bundles groupoids. We build their ajoint bundle groupoids, which we interpret as vector bundle groupoids, widely discussed in the literature. We describe their nerves, which are simplicial objects in the category of principal bundles. Applying this construction to pair groupoids enables us to define the gauge group of the nerve of a gauge groupoid as the gauge group of a principal bundle and to describe the…

## References

SHOWING 1-10 OF 27 REFERENCES

### Atiyah sequence and Gauge transformations of a principal 2-bundle over a Lie groupoid

- MathematicsJournal of Geometry and Physics
- 2022

### Lie algebroid structures on double vector bundles and representation theory of Lie algebroids

- Mathematics
- 2010

### Groupoids and singular foliations

- Mathematics
- 2019

This thesis has two objectives. The first objective is to introduce a notion of equivalence for singular foliations that preserves their transverse geometry and is compatible with the notions of…

### General theory of lie groupoids and lie algebroids

- Mathematics
- 2005

Part I. The General Theory: 1. Lie groupoids: fundamental theory 2. Lie groupoids: algebraic constructions 3. Lie algebroids: fundamental theory 4. Lie algebroids: algebraic constructions Part II.…

### Introduction to Foliations and Lie Groupoids

- Mathematics
- 2003

This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an…

### Quotients of singular foliations and Lie 2-group actions

- MathematicsJournal of Noncommutative Geometry
- 2021

Every singular foliation has an associated topological groupoid, called holonomy groupoid (see arXiv:math/0612370). In this note we exhibit some functorial properties of this assignment: if a…

### Higher gauge theory

- Mathematics
- 2005

Just as gauge theory describes the parallel transport of point particles using connections on bundles, higher gauge theory describes the parallel transport of 1-dimensional objects (e.g. strings)…

### An invitation to higher gauge theory

- Mathematics
- 2011

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge…