Animated topology: Ant walk on the Klein bottle

Description: How does the Klein bottle work? The animation explains this from an ant’s point of view. The object, named after the mathematician Felix Klein, is a topological curiosity–a so-called “non-orientable surface“. Because the Klein bottle is a one-sided surface. So there is no “inside“ and “outside“–in contrast to the surface of a sphere. If an ant walks on the Klein bottle, it can reach any point and cannot be caught inside. The orientation of a surface is a topological property. Topology is a branch of mathematics that deals with global properties of objects that remain unchanged when deformed. Topology helps to explain the interior of quantum materials. The Dresden-Würzburg Cluster of Excellence –Complexity and Topology in Quantum Matter explores new quantum materials in high performance laboratories, revealing surprising phenomena under extreme conditions such as ultra-low temperatures, high pressure, or strong magnetic fields. If these special