The ferromagnetic metal-superconductor heterostructure with interface Rashba spin-orbit hopping is a promising candidate for topological superconductivity. We study the interplay between the interface Rashba hopping and the intrinsic Dresselhaus spin-orbit coupling in this heterostructure, and demonstrate rich topological phases with five distinct Chern numbers. In particular, we find a topological state with a Chern number as large as four in the parameter space of the heterostructure. We calculate the Berry curvatures that construct the Chern numbers, and show that these Berry curvatures induce anomalous thermal Hall transport of the superconducting quasiparticles. We reveal chiral edge states in the topological phases, as well as helical edge states in the trivial phase, and show that the wave functions of these edge states mostly concentrate on the ferrometal layer of the heterostructure.

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