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The degeneracies in the spinor bandstructure of bcc Fe are studied from firstprinciples. We find numerous isolated band touchings carrying chiral charges ofmagnitude one (Weyl points) or two (double-Weyl nodes), as well as nonchiraldegeneracy loops (nodal rings). Some degeneracies are located on symmetry linesor planes in the Brillouin zone and others at generic low-symmetry points,realizing all possible scenarios consistent with the magnetic point group. Weclarify the general theory relating the chiral band touchings to the Chernnumbers of the Fermi sheets enclosing them, and use this approach to determinethe Chern numbers on the Fermi surface of bcc Fe. Although most Fermi sheetsenclose Weyl nodes, in almost all cases the net enclosed charge vanishes forsymmetry reasons, resulting in a vanishing Chern number. The exceptions are twoinversion-symmetric electron pockets along the symmetry line $\Delta$ parallelto the magnetization. Each of them surrounds a single Weyl point, leading toChern numbers of $\pm 1$. These small topological pockets contribute a sizableamount 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.

Chiral degeneracies and Fermi-surface Chern numbers in bcc Fe