  We theoretically investigate topological properties of the one-dimensional
superlattice anyon-Hubbard model, which can be mapped to a superlattice
bose-Hubbard model with an occupation-dependent phase factor by fractional
Jordan-Wigner transformation. The topological anyon-Mott insulator is
identified by topological invariant and edge modes using exact diagonalization
and density-matrix renormalization-group algorithm. When only the statistical
angle is varied and all other parameters are fixed, a statistically induced
topological phase transition can be realized, which provides new insights into
the topological phase transitions. What's more, we give an explanation of the
statistically induced topological phase transition. The topological anyon-Mott
phases can also appear in a variety of superlattice anyon-Hubbard models.
