  We study properties of topological phases by calculating the ground state
degeneracy (GSD) of the 2d Levin-Wen (LW) model. Here it is explicitly shown
that the GSD depends only on the spatial topology of the system. Then we show
that the ground state on a sphere is always non-degenerate. Moreover, we study
an example associated with a quantum group, and show that the GSD on a torus
agrees with that of the doubled Chern-Simons theory, consistent with the
conjectured equivalence between the LW model associated with a quantum group
and the doubled Chern-Simons theory.
