Topological materials become switchable

A donut is not a breakfast roll. Those are two very clearly distinguishable objects: One has a hole, the other does not. In mathematics, the two shapes are said to be topologically different—you cannot transform one into the other by small, continuous deformations. Therefore, the difference between them is robust to perturbations: Even if you knead and bend the bun it still doesn’t look like a donut.