A formalism for describing an all-sky map of the polarization of the c
osmic microwave background is presented. The polarization pattern on t
he sky can be decomposed into two geometrically distinct components. O
ne of these components is not coupled to density inhomogeneities. A no
nzero amplitude for this component of polarization can only be caused
by tensor or vector metric perturbations. This allows unambiguous iden
tification of long-wavelength gravity waves or large-scale vortical fl
ows at the time of last scattering.