  We propose a general principle for the low-energy theory of narrow bands with
concentrated Berry curvature and Fubini-Study metric in the form of a map to
Anderson-"+" models composed of heavy fermions hybridizing and interacting with
semi-metallic modes. This map resolves the obstruction preventing topological
bands from being realized in a local Hamiltonian acting on the low-energy
degrees of freedom. The concentrated quantum geometry is reproduced through
band inversion with a dispersive semi-metal, leaving a nearly flat, trivial
band which becomes the heavy fermion. This representation is natural when the
narrow band is not energetically isolated on the scale of the interaction and
an enlarged Hilbert space is inescapable, but also provides analytical insight
into the projected-interaction limit. First exemplified in twisted bilayer
graphene (TBG), we extend it to (1) the twisted checkerboard, which we find has
a chiral symmetric stable anomaly that forbids a lattice realization at all
energies, and (2) the Lieb lattice with gapless flat bands, where we show the
heavy fermions can be obtained by minimizing a Euclidean instanton action to
saturate its BPS bound. The heavy fermion approach is widely applicable and
physically transparent: heavy electrons carry the strong correlations and
dispersive electrons carry the topology. This simple picture unifies the
dichotomous phenomena observed in TBG and points to connections between moir\'e
and stoichiometric materials.
