Complex sentence: All materials can be classified by a single number, a topological invariant; this is constructed out of the bulk electronic wave functions, which are integrated in over the Brillouin zone, in a similar way that the genus is calculated in geometric topology.
Split into simpler sentences: All materials can be classified by a single number, a so called topological invariant. This topological invariant is constructed out of the bulk electronic wave functions, which are integrated in over the Brillouin zone, in a similar way that the genus is calculated in geometric topology.