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What is topology theory and its application?
Topology is a branch of mathematics that studies spatial morphology, and its research object is the relationship between objects in space, such as connectivity, compactness and homotopy. Topology is widely used in physics, engineering, computer science and other fields.

In physics, topological physics, as a new research direction in the field of condensed matter, not only has profound physical connotations in theory, such as body-edge correspondence, dimensional hierarchy phenomenon, chiral anomaly, etc., but also has topological protection of boundary propagation state, lossless, overcoming defect scattering and novel body transport phenomenon. These new physical effects have laid a solid scientific foundation for people to design and realize subversive materials that break through the limits of traditional technology, and thus have great application prospects in the fields of light, sound and electricity.

In engineering, topology can be used to design new materials and devices. For example, the topological insulator with band gap can realize the charge and spin flow immune to defects; Topologically protected majorana zero-energy mode in topological superconductors is the basis of topological quantum computation. In photonic crystals, phononic crystals and other artificial band gap materials, topological physics has also prompted the design and invention of new devices such as unidirectional propagating light, acoustic waveguide, spin-selective energy beam splitter, photoacoustic isolator, topological laser and topological router.