Topology Concept (IMAGE)
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The topology is a mathematical concept to describe and distinguish the shape or geometry of, e.g., bodies. In physics, this concept is also applied to vector fields such as the magnetization pattern in a thin film. Two bodies have the same topology if they can be transformed into each other only by so-called continuous transformations such as stretching, compressing, bending, and twisting. However, cutting and gluing are not allowed in this context. This leads to the result that a mug and doughnut share the same topology. Just imagine a mug made of modeling clay: When skillfully deforming the clay, it is possible to form the doughnut without cutting or gluing the clay at any point in the process. However, it is impossible to model a doughnut out of aspoon in this way. At some point you will have to cut the doughnut hole or glue two ends of a roll to end up with a doughnut. So spoon and doughnut can be distinguished by their different topology. In physics, it is often assumed that a certain energy barrier has to be overcome in order to change the topology of a system.
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MBI
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