  The Skyrme model is a classical field theory which models the strong
interaction between atomic nuclei. It has to be quantized in order to compare
it to nuclear physics. When the Skyrme model is semi-classically quantized it
is important to take the Finkelstein-Rubinstein constraints into account. The
aim of this paper is to show how to calculate these FR constraints directly
from the rational map ansatz using basic homotopy theory. We then apply this
construction in order to quantize the Skyrme model in the simplest
approximation, the zero mode quantization. This is carried out for up to 22
nucleons, and the results are compared to experiment.
