The spin group is defined as the group of homotopy classes of such paths in the rotation group, and the space of spinors forms a linear representation of it (that is, a vector space on which elements of the group act as linear transformations).
The spin group is defined as the group of homotopy classes of such paths in the rotation group. The space of spinors forms a linear representation of it (that is, a vector space on which elements of the group act as linear transformations).