  Using the new normalized thermodynamic scalar curvature, we investigate the
microstructures and phase transitions of black holes in massive gravity for
horizons of various topologies. We find that the graviton mass enhances the
repulsive interactions of small black holes and weakens the attractive
interactions of large black holes, with possiblity of new repulsive regions for
microstructures in phase space. In addition, the repulsive interactions of
small black hole are strong for spherical topology, followed by flat and
hyperbolic topology; while, the attractive interactions of large black hole are
strong for hyperbolic topology, followed by flat and weakest for spherical
topology.
