Topological Field Theories
Topological Field Theories (TFTs) are a class of quantum field theories that focus on the properties of spaces that remain unchanged under continuous deformations. They are primarily concerned with topological aspects rather than geometric details, making them useful in understanding the underlying structure of various physical systems. TFTs often arise in the study of string theory and quantum gravity.
In a TFT, physical observables depend only on the topology of the underlying space, such as the number of holes or the connectivity of the surface. This leads to interesting applications in mathematics, particularly in knot theory and 3-manifold invariants, where they help classify and distinguish different topological structures.