The properties of topological insulators and their surface states are highly dependent on both the dimension of the material and its underlying symmetries, and can be classified using the so-called periodic table of topological insulators. Some combinations of dimension and symmetries forbid topological insulators completely. All topological insulators have at least U(1) symmetry from particle number conservation, and often have time-reversal symmetry from the absence of a magnetic field. In this way, topological insulators are an example of symmetry-protected topological order. So-called "topological invariants", taking values in Z 2 or Z , allow classification of insulators as trivial or topological, and can be computed by various methods.