  We consider a magnetic skyrmion crystal formed at the surface of a
topological insulator. Incorporating the exchange interaction between the
helical Dirac surface states and the periodic N\'eel or Bloch skyrmion texture,
we obtain the resulting electronic band structure and discuss the constraints
that symmetries impose on the energies and Berry curvature. We find substantive
qualitative differences between the N\'eel and Bloch cases, with the latter
generically permitting a multiband low energy tight-binding representation
whose parameters are tightly constrained by symmetries. We explicitly compute
the associated Wannier orbitals, which resemble the ringlike chiral bound
states of helical Dirac fermions coupled to a single skyrmion in a
ferromagnetic background. We construct a two-band tight-binding model with real
nearest-neighbor hoppings which captures the salient topological features of
the low-energy bands. Our results are relevant to magnetic topological
insulators (TIs), as well as to TI-magnetic thin film heterostructures, in
which skyrmion crystals may be stabilized.
