A generalized definition of spin in non-orientable geometries

Non-orientable nanostructures are becoming feasable today. This lead us to the study of spin in these geometries. Hence a physically sound definition of spin is suggested. Using our definition, we study the question of the number of different ways to define spin. We argue that the possibility of having more than one spin structure should be taken into account energetically. The effect of topology on spin is studied in detail using cohomological arguments. We generalize the definition of equivalence among (s)pin structures to include non-orientable spaces.