  It is well-known that the winding number of the Skyrmion can be identified as
the baryon number. We show in this paper that this result can also be
established using the Atiyah-Singer index theorem and spectral flow arguments.
We argue that this proof suggests that there are light quarks moving in the
field of the Skyrmion. We then show that if these light degrees of freedom are
averaged out, the low energy excitations of the Skyrmion are in fact spinorial.
A natural consequence of our approach is the prediction of a $(1/2)^{-}$ state
and its excitations in addition to the nucleon and delta. Using the recent
numerical evidence for the existence of Skyrmions with discrete spatial
symmetries, we further suggest that the the low energy spectrum of many light
nuclei may possess a parity doublet structure arising from a subtle topological
interaction between the slow Skyrmion and the fast quarks. We also present
tentative experimental evidence supporting our arguments.
