  A linear polarization field on a surface is expressed in terms of scalar
functions, providing an invariant separation into two components; one of these
is the B mode, important as a signature of primordial gravitational waves,
which would lend support to the inflation hypothesis. The case of a plane
already exhibits the key ideas, including the formal analogy with a vector
field decomposed into gradient plus curl, with the B mode like the latter. The
formalism is generalized to a spherical surface using cartesian coordinates.
Analysis of global data provides a path to vector and tensor spherical
harmonics.
