  We propose to use generic Chern numbers for a characterization of topological
insulators. It is suitable for a numerical characterization of low dimensional
quantum liquids where strong quantum fluctuations prevent from developing
conventional orders. By twisting parameters of boundary conditions, the
non-Abelian Chern number are defined for a few low lying states near the ground
state in a finite system, which is a ground state multiplet with a possible
(topological) degeneracy. We define the system as a topological insulator when
energies of the multiplet are well separated from the above. Translational
invariant twists up to a unitary equivalence are crutial to pick up only bulk
properties without edge states. As a simple example, the setup is applied for a
two-dimensional $XXZ$-spin system with an ising anisotropy where the ground
state multiplet is composed of doubly almost degenerate states. It gives a
vanishing Chern number due to a symmetry. Also Chern numbers for the generic
fractional quantum Hall states are discussed shortly.
