Measuring topological order

The topological order of a (2 + 1)D topological phase of matter is characterized by its chiral central charge and a unitary modular tensor category that describes the universal fusion and braiding properties of its anyonic quasiparticles. I discuss the topologically invariant quantities associated with these and identify ones that are useful for determining the topological order. I propose a variety of physical experiments that probe these quantities and detail the relation of the measured data to the topological invariants.