Fadell-Neuwirth extension

The Fadell-Neuwirth extension is a concept in topology that describes how the configuration space of multiple points on a surface relates to the space with fewer points. It shows how adding a new point to a set of existing points on a surface creates a structured way to understand the possible arrangements. Specifically, it provides a method to extend the understanding of how points can move without colliding, by relating larger configuration spaces to smaller ones through a fiber bundle—a mathematical tool that models a space as layers built over a base space.