Our project aim is to investigate the different types of point-like and loop / string-like topologically excited states arising in higher gauge theory lattice models for (3+1)-dimensional topological phases of matter, categorifying Kitaev quantum double model for (2+1)-dimensional topological phases.
A central topic of this project concerns analysing the behaviour of loop excitations when they move in three-dimensional space, braid and interact, and explore applications to topological quantum computing and to knot theory in four dimensions.