  We explain why, in a configuration space that is multiply connected, i.e.,
whose fundamental group is nontrivial, there are several quantum theories,
corresponding to different choices of topological factors. We do this in the
context of Bohmian mechanics, a quantum theory without observers from which the
quantum formalism can be derived. What we do can be regarded as generalizing
the Bohmian dynamics on $\mathbb{R}^{3N}$ to arbitrary Riemannian manifolds,
and classifying the possible dynamics that arise. This approach provides a new
understanding of the topological features of quantum theory, such as the
symmetrization postulate for identical particles. For our analysis we employ
wave functions on the universal covering space of the configuration space.
