A sphere and a cube can be deformed into one another without cuts or stitches. A mug and a glass cannot because, to deform the first into the second, the handle needs to be broken. Topology is the branch of mathematics that formalizes this difference between mugs and glasses, extending it also to abstract spaces with many dimensions. A new theory developed by scientists at SISSA in Trieste has succeeded in establishing a new relationship between the presence or absence of ‘handles’ in the space of the arrangements of atoms and molecules that make up a material, and the propensity of the latter to conduct electricity. According to this theory, the insulating materials ‘equipped with handles’ can conduct electricity as well as metals, while retaining typical properties of insulators, such as transparency.
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Source: Phys.org