  The mixed-valence compound SmB6 with partially filled samarium 4f flat bands
hybridizing with 5d conduction bands is a paramount example of a correlated
topological heavy-fermion system. In this study we revisit the topology of SmB6
with the band theory paradigm and uncover previously overlooked aspects
resulting from the formation of multiple topological gaps in the electronic
structure. By invoking topological quantum chemistry (TQC) we provide a
detailed classification of the strong and crystalline topological features that
derive from the existence of such topological gaps. To corroborate this
classification, we calculate Wilson loops and simulate the surface electronic
structure using a minimal tight-binding model, allowing us to describe its
surface states and confirm the crystalline topology. We finally discuss its
implications for experiments.
