  The degeneracies in the spinor bandstructure of bcc Fe are studied from first
principles. We find numerous isolated band touchings carrying chiral charges of
magnitude one (Weyl points) or two (double-Weyl nodes), as well as nonchiral
degeneracy loops (nodal rings). Some degeneracies are located on symmetry lines
or planes in the Brillouin zone and others at generic low-symmetry points,
realizing all possible scenarios consistent with the magnetic point group. We
clarify the general theory relating the chiral band touchings to the Chern
numbers of the Fermi sheets enclosing them, and use this approach to determine
the Chern numbers on the Fermi surface of bcc Fe. Although most Fermi sheets
enclose Weyl nodes, in almost all cases the net enclosed charge vanishes for
symmetry reasons, resulting in a vanishing Chern number. The exceptions are two
inversion-symmetric electron pockets along the symmetry line $\Delta$ parallel
to the magnetization. Each of them surrounds a single Weyl point, leading to
Chern numbers of $\pm 1$. These small topological pockets contribute a sizable
amount to the nonquantized part of the intrinsic anomalous Hall conductivity,
proportional to their reciprocal-space separation. Variation of the Fermi level
(or other system parameters) may lead to a touching event between Fermi sheets,
accompanied by a transfer of Chern number between them.
