# Estimates of the amplitude of holonomies by the curvature of a connection on a bundle

## TL;DR

This paper demonstrates that the magnitude of holonomies in a vector bundle can be bounded using the surface integral of the connection's curvature, linking geometric curvature to holonomy amplitude.

## Contribution

It introduces a method to estimate holonomy amplitudes based on curvature integrals, providing a new geometric control tool.

## Key findings

- Holonomy amplitude can be bounded by curvature integral.
- Curvature of a connection influences holonomy size.
- Provides a geometric estimate linking curvature and holonomy.

## Abstract

We show how the amplitude of holonomies on a vector bundle can be controlled by the integral of the curvature of the connection on a surface enclosed by the curve.