  We construct theoretical models for two dimensional(2d) chiral
$d_{x^2-y^2}\pm id_{xy}$ topological superconductors and for three
dimensional(3d) $d$ wave topological superconductors. Moreover we build models
for any 2d class C and 3d class CI topological superconductors (with any even
topological invariants). We also construct concrete models that can realize
quantum anomalous Hall effect with arbitrary large Chern numbers. We study the
chiral edge modes or gapless surface states of our 2d or 3d models in details.
In all the cases, we find novel mechanisms that make the numbers of boundary
states always agree with the nontrivial bulk topology, just as required by the
bulk boundary correspondence.
