Topology in Physics: Donuts, Holes, and Exotic Matter

Topology studies shapes and spaces that can stretch or bend but not tear or glue.
A donut and a coffee mug are topologically the same because each has one hole.
Physics uses topology to classify states of matter beyond solids, liquids, and gases.
Topological insulators conduct electricity on their surfaces but not inside.
Magnetic fields can form stable knots and vortices thanks to topological rules.
In cosmology, topology helps explore possible shapes of the entire universe.
Superfluids and superconductors often exhibit topological properties.
The quantum Hall effect is a famous topological phenomenon in condensed matter physics.
Topological ideas help protect quantum information from errors in quantum computing.
At its heart, topology reveals that “holes” and connectivity can shape the laws of physics.