Topological theory of physical fields

We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid disk. If tearing or gluing get involved, i.e. the deformation is not continuous anymore, the initial topology will consequently change giving rise to a topologically distinct object, e.g., a torus. This simple …