A formalism for describing an all-sky map of the polarization of the cosmic microwave background is presented. The polarization pattern on the sky can be decomposed into two geometrically distinct components. One of these components is not coupled to density inhomogeneities. A nonzero amplitude for this component of polarization can only be caused by tensor or vector metric perturbations. This allows unambiguous identification of long-wavelength gravity waves or large-scale vortical flows at the time of last scattering.