 Any manifold modeled on formula_14 is orientable, and is a circle bundle over some 2-dimensional hyperbolic orbifold (a Seifert fiber space).Under this covering, the preimage of the modular group PSL(2,Z) is the braid group on 3 generators, "B"3, which is the universal central extension of the modular group.These are lattices inside the relevant algebraic groups, and this corresponds algebraically to the universal covering group in topology.