  We study theoretically the role of topological invariants to protect the
Majorana fermions in a model of two-dimensional chiral superconductors which
belong to class D of topological periodic table. A rich phase diagram is
revealed. Each phase is characterized by the topological invariants for 2d (Z)
and 1d (Z2), which lead to the Majorana fermion at the edge of the dislocation
and the core of the vortex. Interference of the Majorana fermions originated
from the different topological invariants is studied. The stability of the
Majorana fermion with respect to the interlayer coupling, i.e., in 3d, is also
examined.
