# Asymptotic expansions of holonomy

## TL;DR

This paper derives gauge-independent asymptotic expansions for the holonomy of loops in principal bundles, expressed in terms of loop length within Riemannian or sub-Riemannian geometries.

## Contribution

It provides a novel gauge-independent asymptotic formula for holonomy based on loop length in various geometric structures.

## Key findings

- Derived an asymptotic expansion formula for holonomy
- The formula is independent of gauge choice
- Applicable to Riemannian and sub-Riemannian structures

## Abstract

Given a principal bundle with a connection, we look for an asymptotic expansion of the holonomy of a loop in terms of its length. This length is defined relative to some Riemannian or sub-Riemannian structure. We are able to give an asymptotic formula that is independent of choice of gauge.