What are Fiber Bundles?
Understanding Fiber Bundles
A fiber bundle is a space that is locally a product space but may have different global topological structure.
In simple terms, fiber bundles provide a convenient way to take products of topological spaces. This can be used to build complex spaces from simpler spaces.
Examples
The Möbius strip is a nontrivial bundle over the circle.
Another nontrivial bundle is the Klein bottle, which can be viewed as a “twisted” circle bundle over another circle.
Fiber bundles are used in physics to represent Gauge theories and constrained vector fields. More specifically, fiber bundles are important global structures in physical fields and are thus relevant to Gauge theories in electricity and magnetism, quantum electrodynamics, quantum chromodynamics and consequently Yang-mills theory.
I hope this post inspires you to learn more about these fascinating topological structures. Thank you for reading!
